• Previous Article
    Several new classes of (balanced) Boolean functions with few Walsh transform values
  • AMC Home
  • This Issue
  • Next Article
    An explicit representation and enumeration for negacyclic codes of length $ 2^kn $ over $ \mathbb{Z}_4+u\mathbb{Z}_4 $
doi: 10.3934/amc.2020081

Internal state recovery of Espresso stream cipher using conditional sampling resistance and TMDTO attack

Bosch India (RBEI/ESY), Bangalore, India

Received  November 2019 Revised  January 2020 Published  April 2020

Espresso is a stream cipher proposed for the 5G wireless communication system. Since the design of this cipher is based on the Galois configuration of NLFSR, the cipher has a short propagation delay, and it is the fastest among the ciphers below 1500 GE, including Grain-128 and Trivium. The time-memory-data tradeoff (TMDTO) attack on this cipher and finding the conditional BSW sampling resistance are difficult due to its Galois configuration. This paper demonstrates the calculation of conditional BSW-sampling resistance of Espresso stream cipher, which is based on Galois configuration, and also mounts the TMDTO attack on the cipher by employing the calculated sampling resistance. It is also shown that the attack complexities of TMDTO attack are lower than those claimed by the designers of the ciphers.

Citation: Nishant Sinha. Internal state recovery of Espresso stream cipher using conditional sampling resistance and TMDTO attack. Advances in Mathematics of Communications, doi: 10.3934/amc.2020081
References:
[1]

S. Babbage, A space/time tradeoff in exhaustive search attacks on stream ciphers, European Convention on Security and Detection, 408 (1995). Google Scholar

[2]

A. Biryukov and A. Shamir, Cryptanalytic time/memory/data tradeoffs for stream ciphers, ASIACRYPT 2000, Lecture Notes in Computer Science, 1976 (2000), 1-13.  doi: 10.1007/3-540-44448-3_1.  Google Scholar

[3]

A. BiryukovA. Shamir and D. Wagner, Real time cryptanalysis of A5/1 on a PC, Fast Software Encryption 2000, Lecture Notes in Computer Science, 1978 (2001), 37-44.  doi: 10.1007/3-540-44706-7_1.  Google Scholar

[4]

T. E. Bjørstad, Cryptanalysis of grain using time/memory/data tradeoffs, (2008). Available from: http://www.ecrypt.eu.org/stream/grainp3.html. Google Scholar

[5]

C. Cannière and B. Preneel, Trivium, new stream cipher designs: The eSTREAM finalists, Lecture Notes in Computer Science, 4986 (2008), 244-266.   Google Scholar

[6]

E. Dubrova, A transformation from the Fibonacci to the Galois NLFSRs, IEEE Transactions on Information Theory, 55 (2009), 5263-5271.  doi: 10.1109/TIT.2009.2030467.  Google Scholar

[7]

E. Dubrova and M. Hell, A stream cipher for 5G wireless communications systems, Cryptography and Communications, 9 (2017), 273-289.  doi: 10.1007/s12095-015-0173-2.  Google Scholar

[8]

J. Golić, Cryptanalysis of alleged $A5$ stream cipher, EUROCRYPT 1997, Lecture Notes in Computer Science, 1233 (1997), 239-255.   Google Scholar

[9]

M. HellT. JohanssonA. Maximov and W. Meier, The Grain family of stream ciphers, new stream cipher designs: The eSTREAM finalists, Lecture Notes in Computer Science, 4986 (2008), 17-190.   Google Scholar

[10]

M. E. Hellman, A cryptanalytic time-memory trade-off, IEEE Transactions on Information Theory, 26 (1980), 401-406.  doi: 10.1109/TIT.1980.1056220.  Google Scholar

[11]

J. Hong and P. Sarkar, New applications of time memory data tradeoffs, ASIACRYPT 2005, Lecture Notes in Computer Science, Springer, Berlin, 3788 (2005), 353-372.  doi: 10.1007/11593447_19.  Google Scholar

[12]

S. MaitraN. SinhaA. SiddhantiR. Anand and S. Gangopadhyay, A TMDTO attack against Lizard, IEEE Transactions on Computers, 67 (2018), 733-739.  doi: 10.1109/TC.2017.2773062.  Google Scholar

[13]

M. J. MihaljevićS. GangopadhyayG. Paul and H. Imai, Internal state recovery of Grain-v1 employing normality order of the filter function, IET Information Security, 6 (2012), 55-64.   Google Scholar

[14]

M. J. MihaljevićS. GangopadhyayG. Paul and H. Imai, Generic cryptographic weakness of k-normal Boolean functions in certain stream ciphers and cryptanalysis of Grain-128, Periodica Mathematica Hungarica, 65 (2012), 205-227.  doi: 10.1007/s10998-012-4631-8.  Google Scholar

show all references

References:
[1]

S. Babbage, A space/time tradeoff in exhaustive search attacks on stream ciphers, European Convention on Security and Detection, 408 (1995). Google Scholar

[2]

A. Biryukov and A. Shamir, Cryptanalytic time/memory/data tradeoffs for stream ciphers, ASIACRYPT 2000, Lecture Notes in Computer Science, 1976 (2000), 1-13.  doi: 10.1007/3-540-44448-3_1.  Google Scholar

[3]

A. BiryukovA. Shamir and D. Wagner, Real time cryptanalysis of A5/1 on a PC, Fast Software Encryption 2000, Lecture Notes in Computer Science, 1978 (2001), 37-44.  doi: 10.1007/3-540-44706-7_1.  Google Scholar

[4]

T. E. Bjørstad, Cryptanalysis of grain using time/memory/data tradeoffs, (2008). Available from: http://www.ecrypt.eu.org/stream/grainp3.html. Google Scholar

[5]

C. Cannière and B. Preneel, Trivium, new stream cipher designs: The eSTREAM finalists, Lecture Notes in Computer Science, 4986 (2008), 244-266.   Google Scholar

[6]

E. Dubrova, A transformation from the Fibonacci to the Galois NLFSRs, IEEE Transactions on Information Theory, 55 (2009), 5263-5271.  doi: 10.1109/TIT.2009.2030467.  Google Scholar

[7]

E. Dubrova and M. Hell, A stream cipher for 5G wireless communications systems, Cryptography and Communications, 9 (2017), 273-289.  doi: 10.1007/s12095-015-0173-2.  Google Scholar

[8]

J. Golić, Cryptanalysis of alleged $A5$ stream cipher, EUROCRYPT 1997, Lecture Notes in Computer Science, 1233 (1997), 239-255.   Google Scholar

[9]

M. HellT. JohanssonA. Maximov and W. Meier, The Grain family of stream ciphers, new stream cipher designs: The eSTREAM finalists, Lecture Notes in Computer Science, 4986 (2008), 17-190.   Google Scholar

[10]

M. E. Hellman, A cryptanalytic time-memory trade-off, IEEE Transactions on Information Theory, 26 (1980), 401-406.  doi: 10.1109/TIT.1980.1056220.  Google Scholar

[11]

J. Hong and P. Sarkar, New applications of time memory data tradeoffs, ASIACRYPT 2005, Lecture Notes in Computer Science, Springer, Berlin, 3788 (2005), 353-372.  doi: 10.1007/11593447_19.  Google Scholar

[12]

S. MaitraN. SinhaA. SiddhantiR. Anand and S. Gangopadhyay, A TMDTO attack against Lizard, IEEE Transactions on Computers, 67 (2018), 733-739.  doi: 10.1109/TC.2017.2773062.  Google Scholar

[13]

M. J. MihaljevićS. GangopadhyayG. Paul and H. Imai, Internal state recovery of Grain-v1 employing normality order of the filter function, IET Information Security, 6 (2012), 55-64.   Google Scholar

[14]

M. J. MihaljevićS. GangopadhyayG. Paul and H. Imai, Generic cryptographic weakness of k-normal Boolean functions in certain stream ciphers and cryptanalysis of Grain-128, Periodica Mathematica Hungarica, 65 (2012), 205-227.  doi: 10.1007/s10998-012-4631-8.  Google Scholar

Table 1.  State Bits required to calculate feedback bits
Row Feedback bit calculaton because of (5) Column 0 Feedback bit calculaton because of (6) Column 1 Feedback bit calculaton because of (7) Column 2 Feedback bit calculaton because of (8) Column 3 Feedback bit calculaton because of (9) Column 4
Feedback bits State bits appeared on RHS of (5) Feedback bits State bits appeared on RHS of (6) Feedback bits State bits appeared on RHS of (7) Feedback bits State bits appeared on RHS of (8) Feedback bits State bits appeared on RHS of (2)
0 $ x_{256}^0 $ $ x_{0}, \underline{x_{41}}, \overline{x_{70}} $ $ x_{252}^1 $ $ x_{252}, x_{42}, $ $ x_{83}, x_{8} $ $ x_{248}^2 $ $ x_{248}, x_{44}, $ $ x_{102}, x_{40} $ $ x_{244}^3 $ $ x_{244}, x_{43}, $ $ x_{118}, x_{103} $ $ x_{240}^4 $ $ x_{240}, \overline{x_{46}}, $ $ \underline{x_{141}}, x_{117} $
1 $ x_{257}^0 $ $ x_{1}, \underline{x_{42}}, \overline{x_{71}} $ $ x_{253}^1 $ $ x_{253}, x_{43}, $ $ x_{84}, x_{9} $ $ x_{249}^2 $ $ x_{249}, x_{45}, $ $ x_{103}, x_{41} $ $ x_{245}^3 $ $ x_{245}, x_{44}, $ $ x_{119}, x_{104} $ $ x_{241}^4 $ $ x_{241}, \overline{x_{47}}, $ $ \underline{x_{142}}, x_{118} $
2 $ x_{258}^0 $ $ x_{2}, \underline{x_{43}}, \overline{x_{72}} $ $ x_{254}^1 $ $ x_{254}, x_{44}, $ $ x_{85}, x_{10} $ $ x_{250}^2 $ $ x_{250}, \overline{x_{46}}, $ $ \underline{x_{104}}, x_{42} $ $ x_{246}^3 $ $ x_{246}, x_{45}, $ $ x_{120}, x_{105} $ $ x_{242}^4 $ $ x_{242}, \overline{x_{48}}, $ $ \underline{x_{143}}, x_{119} $
3 $ x_{259}^0 $ $ x_{3}, \underline{x_{44}}, \overline{x_{73}} $ $ x_{255}^1 $ $ x_{255}, x_{45}, $ $ x_{86}, x_{11} $ $ x_{251}^2 $ $ x_{251}, \overline{x_{47}}, $ $ \underline{x_{105}}, x_{43} $ $ x_{247}^3 $ $ x_{247}, \overline{x_{46}}, $ $ \underline{x_{121}}, x_{106} $ $ x_{243}^4 $ $ x_{243}, \overline{x_{49}}, $ $ \underline{x_{144}}, x_{120} $
4 $ x_{260}^0 $ $ x_{4}, \underline{x_{45}}, \overline{x_{74}} $ $ x_{256}^1 $ $ x_{256}^0, \overline{x_{46}}, $ $ \underline{x_{87}}, x_{12} $ $ x_{252}^2 $ $ x_{252}^1, \overline{x_{48}}, $ $ \underline{x_{106}}, x_{44} $ $ x_{248}^3 $ $ x_{248}^2, \overline{x_{47}}, $ $ \underline{x_{122}}, x_{107} $ $ x_{244}^4 $ $ x_{244}^3, \overline{x_{50}}, $ $ \underline{x_{145}}, x_{121} $
5 $ x_{261}^0 $ $ x_{5}, \overline{x_{46}}, \overline{x_{75}} $ $ x_{257}^1 $ $ x_{257}^0, \overline{x_{47}}, $ $ \underline{x_{88}}, x_{13} $ $ x_{253}^2 $ $ x_{253}^1, \overline{x_{49}}, $ $ \underline{x_{107}}, x_{45} $ $ x_{249}^3 $ $ x_{249}^2, \overline{x_{48}}, $ $ \underline{x_{123}}, x_{108} $ $ x_{245}^4 $ $ x_{245}^3, \overline{x_{51}}, $ $ \underline{x_{146}}, x_{122} $
6 $ x_{262}^0 $ $ x_{6}, \overline{x_{47}}, \overline{x_{76}} $ $ x_{258}^1 $ $ x_{258}^0, \overline{x_{48}}, $ $ \underline{x_{89}}, x_{14} $ $ x_{254}^2 $ $ x_{254}^1, \overline{x_{50}}, $ $ \underline{x_{108}}, \overline{x_{46}} $ $ x_{250}^3 $ $ x_{250}^2, \overline{x_{49}}, $ $ \underline{x_{124}}, x_{109} $ $ x_{246}^4 $ $ x_{246}^3, \overline{x_{52}}, $ $ \underline{x_{147}}, x_{123} $
7 $ x_{263}^0 $ $ x_{7}, \overline{x_{48}}, \underline{x_{77}} $ $ x_{259}^1 $ $ x_{259}^0, \overline{x_{49}}, $ $ \underline{x_{90}}, x_{15} $ $ x_{255}^2 $ $ x_{255}^1, \overline{x_{51}}, $ $ \underline{x_{109}}, \overline{x_{47}} $ $ x_{251}^3 $ $ x_{251}^2, \overline{x_{50}}, $ $ \underline{x_{125}}, x_{110} $ $ x_{247}^4 $ $ x_{247}^3, \overline{x_{53}}, $ $ \underline{x_{148}}, x_{124} $
8 $ x_{264}^0 $ $ x_{8}, \overline{x_{49}}, \underline{x_{78}} $ $ x_{260}^1 $ $ x_{260}^0, \overline{x_{50}}, $ $ \underline{x_{91}}, x_{16} $ $ x_{256}^2 $ $ x_{256}^1, \overline{x_{52}}, $ $ \underline{x_{110}}, \overline{x_{48}} $ $ x_{252}^3 $ $ x_{252}^2, \overline{x_{51}}, $ $ \underline{x_{126}}, x_{111} $ $ x_{248}^4 $ $ x_{248}^3, \overline{x_{54}}, $ $ \underline{x_{149}}, x_{125} $
9 $ x_{265}^0 $ $ x_{9}, \overline{x_{50}}, \underline{x_{79}} $ $ x_{261}^1 $ $ x_{261}^0, \overline{x_{51}}, $ $ \underline{x_{92}}, x_{17} $ $ x_{257}^2 $ $ x_{257}^1, \overline{x_{53}}, $ $ \underline{x_{111}}, \overline{x_{49}} $ $ x_{253}^3 $ $ x_{253}^2, \overline{x_{52}}, $ $ \underline{x_{127}}, x_{112} $ $ x_{249}^4 $ $ x_{249}^3, \overline{x_{55}}, $ $ \underline{x_{150}}, x_{126} $
10 $ x_{266}^0 $ $ x_{10}, \overline{x_{51}}, \underline{x_{80}} $ $ x_{262}^1 $ $ x_{262}^0, \overline{x_{52}}, $ $ \underline{x_{93}}, x_{18} $ $ x_{258}^2 $ $ x_{258}^1, \overline{x_{54}}, $ $ \underline{x_{112}}, \overline{x_{50}} $ $ x_{254}^3 $ $ x_{254}^2, \overline{x_{53}}, $ $ \underline{x_{128}}, x_{113} $ $ x_{250}^4 $ $ x_{250}^3, \overline{x_{56}}, $ $ \underline{x_{151}}, x_{127} $
11 $ x_{267}^0 $ $ x_{11}, \overline{x_{52}}, \underline{x_{81}} $ $ x_{263}^1 $ $ x_{263}^0, \overline{x_{53}}, $ $ \underline{x_{94}}, x_{19} $ $ x_{259}^2 $ $ x_{259}^1, \overline{x_{55}}, $ $ \underline{x_{113}}, \overline{x_{51}} $ $ x_{255}^3 $ $ x_{255}^2, \overline{x_{54}}, $ $ \underline{x_{129}}, x_{114} $ $ x_{251}^4 $ $ x_{251}^3, \overline{x_{57}}, $ $ \underline{x_{152}}, x_{128} $
12 $ x_{268}^0 $ $ x_{12}, \overline{x_{53}}, \underline{x_{82}} $ $ x_{264}^1 $ $ x_{264}^0, \overline{x_{54}}, $ $ \underline{x_{95}}, x_{20} $ $ x_{260}^2 $ $ x_{260}^1, \overline{x_{56}}, $ $ \underline{x_{114}}, \overline{x_{52}} $ $ x_{256}^3 $ $ x_{256}^2, \overline{x_{55}}, $ $ \underline{x_{130}}, x_{115} $ $ x_{252}^4 $ $ x_{252}^3, \overline{x_{58}}, $ $ \underline{x_{153}}, x_{129} $
13 $ x_{269}^0 $ $ x_{13}, \overline{x_{54}}, \underline{x_{83}} $ $ x_{265}^1 $ $ x_{265}^0, \overline{x_{55}}, $ $ \underline{x_{96}}, x_{21} $ $ x_{261}^2 $ $ x_{261}^1, \overline{x_{57}}, $ $ \underline{x_{115}}, \overline{x_{53}} $ $ x_{257}^3 $ $ x_{257}^2, \overline{x_{56}}, $ $ \underline{x_{131}}, x_{116} $ $ x_{253}^4 $ $ x_{253}^3, \overline{x_{59}}, $ $ \underline{x_{154}}, x_{130} $
14 $ x_{270}^0 $ $ x_{14}, \overline{x_{55}}, \underline{x_{84}} $ $ x_{266}^1 $ $ x_{266}^0, \overline{x_{56}}, $ $ \underline{x_{97}}, x_{22} $ $ x_{262}^2 $ $ x_{262}^1, \overline{x_{58}}, $ $ \underline{x_{116}}, \overline{x_{54}} $ $ x_{258}^3 $ $ x_{258}^2, \overline{x_{57}}, $ $ \underline{x_{132}}, x_{117} $ $ x_{254}^4 $ $ x_{254}^3, \overline{x_{60}}, $ $ \underline{x_{155}}, x_{131} $
15 $ x_{271}^0 $ $ x_{15}, \overline{x_{56}}, \underline{x_{85}} $ $ x_{267}^1 $ $ x_{267}^0, \overline{x_{57}}, $ $ \underline{x_{98}}, x_{23} $ $ x_{263}^2 $ $ x_{263}^1, \overline{x_{59}}, $ $ \underline{x_{117}}, \overline{x_{55}} $ $ x_{259}^3 $ $ x_{259}^2, \overline{x_{58}}, $ $ \underline{x_{133}}, x_{118} $ $ x_{255}^4 $ $ x_{255}^3, \overline{x_{61}}, $ $ \underline{x_{156}}, x_{132} $
16 $ x_{272}^0 $ $ x_{16}, \overline{x_{57}}, \underline{x_{86}} $ $ x_{268}^1 $ $ x_{268}^0, \overline{x_{58}}, $ $ \underline{x_{99}}, x_{24} $ $ x_{264}^2 $ $ x_{264}^1, \overline{x_{60}}, $ $ \underline{x_{118}}, \overline{x_{56}} $ $ x_{260}^3 $ $ x_{260}^2, \overline{x_{59}}, $ $ \underline{x_{134}}, x_{119} $ $ x_{256}^4 $ $ x_{256}^3, \overline{x_{62}}, $ $ \underline{x_{157}}, x_{133} $
17 $ x_{273}^0 $ $ x_{17}, \overline{x_{58}}, \underline{x_{87}} $ $ x_{269}^1 $ $ x_{269}^0, \overline{x_{59}}, $ $ \underline{x_{100}}, x_{25} $ $ x_{265}^2 $ $ x_{265}^1, \overline{x_{61}}, $ $ \underline{x_{119}}, \overline{x_{57}} $ $ x_{261}^3 $ $ x_{261}^2, \overline{x_{60}}, $ $ \underline{x_{135}}, x_{120} $ $ x_{257}^4 $ $ x_{257}^3, \overline{x_{63}}, $ $ \underline{x_{158}}, x_{134} $
18 $ x_{274}^0 $ $ x_{18}, \overline{x_{59}}, \underline{x_{88}} $ $ x_{270}^1 $ $ x_{270}^0, \overline{x_{60}}, $ $ \underline{x_{101}}, x_{26} $ $ x_{266}^2 $ $ x_{266}^1, \overline{x_{62}}, $ $ \underline{x_{120}}, \overline{x_{58}} $ $ x_{262}^3 $ $ x_{262}^2, \overline{x_{61}}, $ $ \underline{x_{136}}, x_{121} $ $ x_{258}^4 $ $ x_{258}^3, \overline{x_{64}}, $ $ \underline{x_{159}}, x_{135} $
19 $ x_{275}^0 $ $ x_{19}, \overline{x_{60}}, \underline{x_{89}} $ $ x_{271}^1 $ $ x_{271}^0, \overline{x_{61}}, $ $ \underline{x_{102}}, x_{27} $ $ x_{267}^2 $ $ x_{267}^1, \overline{x_{63}}, $ $ \underline{x_{121}}, \overline{x_{59}} $ $ x_{263}^3 $ $ x_{263}^2, \overline{x_{62}}, $ $ \underline{x_{137}}, x_{122} $ $ x_{259}^4 $ $ x_{259}^3, \overline{x_{65}}, $ $ \underline{x_{160}}, x_{136} $
20 $ x_{276}^0 $ $ x_{20}, \overline{x_{61}}, \underline{x_{90}} $ $ x_{272}^1 $ $ x_{272}^0, \overline{x_{62}}, $ $ \underline{x_{103}}, x_{28} $ $ x_{268}^2 $ $ x_{268}^1, \overline{x_{64}}, $ $ \underline{x_{122}}, \overline{x_{60}} $ $ x_{264}^3 $ $ x_{264}^2, \overline{x_{63}}, $ $ \underline{x_{138}}, x_{123} $ $ x_{260}^4 $ $ x_{260}^3, \overline{x_{66}}, $ $ \underline{x_{161}}, x_{137} $
21 $ x_{277}^0 $ $ x_{21}, \overline{x_{62}}, \underline{x_{91}} $ $ x_{273}^1 $ $ x_{273}^0, \overline{x_{63}}, $ $ \underline{x_{104}}, x_{29} $ $ x_{269}^2 $ $ x_{269}^1, \overline{x_{65}}, $ $ \underline{x_{123}}, \overline{x_{61}} $ $ x_{265}^3 $ $ x_{265}^2, \overline{x_{64}}, $ $ \underline{x_{139}}, x_{124} $ $ x_{261}^4 $ $ x_{261}^3, \overline{x_{67}}, $ $ \underline{x_{162}}, x_{138} $
22 $ x_{278}^0 $ $ x_{22}, \overline{x_{63}}, \underline{x_{92}} $ $ x_{274}^1 $ $ x_{274}^0, \overline{x_{64}}, $ $ \underline{x_{105}}, x_{30} $ $ x_{270}^2 $ $ x_{270}^1, \overline{x_{66}}, $ $ \underline{x_{124}}, \overline{x_{62}} $ $ x_{266}^3 $ $ x_{266}^2, \overline{x_{65}}, $ $ \underline{x_{140}}, x_{125} $ $ x_{262}^4 $ $ x_{262}^3, \overline{x_{68}}, $ $ \underline{x_{163}}, x_{139} $
23 $ x_{279}^0 $ $ x_{23}, \overline{x_{64}}, \underline{x_{93}} $ $ x_{275}^1 $ $ x_{275}^0, \overline{x_{65}}, $ $ \underline{x_{106}}, x_{31} $ $ x_{271}^2 $ $ x_{271}^1, \overline{x_{67}}, $ $ \underline{x_{125}}, \overline{x_{63}} $ $ x_{267}^3 $ $ x_{267}^2, \overline{x_{66}}, $ $ \underline{x_{141}}, x_{126} $ $ x_{263}^4 $ $ x_{263}^3, \overline{x_{69}}, $ $ \underline{x_{164}}, x_{140} $
24 $ x_{280}^0 $ $ x_{24}, \overline{x_{65}}, \underline{x_{94}} $ $ x_{276}^1 $ $ x_{276}^0, \overline{x_{66}}, $ $ \underline{x_{107}}, x_{32} $ $ x_{272}^2 $ $ x_{272}^1, \overline{x_{68}}, $ $ \underline{x_{126}}, \overline{x_{64}} $ $ x_{268}^3 $ $ x_{268}^2, \overline{x_{67}}, $ $ \underline{x_{142}}, x_{127} $ $ x_{264}^4 $ $ x_{264}^3, \overline{x_{70}}, $ $ \underline{x_{165}}, x_{141} $
25 $ x_{281}^0 $ $ x_{25}, \overline{x_{66}}, \underline{x_{95}} $ $ x_{277}^1 $ $ x_{277}^0, \overline{x_{67}}, $ $ \underline{x_{108}}, x_{33} $ $ x_{273}^2 $ $ x_{273}^1, \overline{x_{69}}, $ $ \underline{x_{127}}, \overline{x_{65}} $ $ x_{269}^3 $ $ x_{269}^2, \overline{x_{68}}, $ $ \underline{x_{143}}, x_{128} $ $ x_{265}^4 $ $ x_{265}^3, \overline{x_{71}}, $ $ \underline{x_{166}}, x_{142} $
26 $ x_{282}^0 $ $ x_{26}, \overline{x_{67}}, \underline{x_{96}} $ $ x_{278}^1 $ $ x_{278}^0, \overline{x_{68}}, $ $ \underline{x_{109}}, x_{34} $ $ x_{274}^2 $ $ x_{274}^1, \overline{x_{70}}, $ $ \underline{x_{128}}, \overline{x_{66}} $ $ x_{270}^3 $ $ x_{270}^2, \overline{x_{69}}, $ $ \underline{x_{144}}, x_{129} $ $ x_{266}^4 $ $ x_{266}^3, \overline{x_{72}}, $ $ \underline{x_{167}}, x_{143} $
27 $ x_{283}^0 $ $ x_{27}, \overline{x_{68}}, \underline{x_{97}} $ $ x_{279}^1 $ $ x_{279}^0, \overline{x_{69}}, $ $ \underline{x_{110}}, x_{35} $ $ x_{275}^2 $ $ x_{275}^1, \overline{x_{71}}, $ $ \underline{x_{129}}, \overline{x_{67}} $ $ x_{271}^3 $ $ x_{271}^2, \overline{x_{70}}, $ $ \underline{x_{145}}, x_{130} $ $ x_{267}^4 $ $ x_{267}^3, \overline{x_{73}}, $ $ \underline{x_{168}}, x_{144} $
28 $ x_{284}^0 $ $ x_{28}, \overline{x_{69}}, \underline{x_{98}} $ $ x_{280}^1 $ $ x_{280}^0, \overline{x_{70}}, $ $ \underline{x_{111}}, x_{36} $ $ x_{276}^2 $ $ x_{276}^1, \overline{x_{72}}, $ $ \underline{x_{130}}, \overline{x_{68}} $ $ x_{272}^3 $ $ x_{272}^2, \overline{x_{71}}, $ $ \underline{x_{146}}, x_{131} $ $ x_{268}^4 $ $ x_{268}^3, \overline{x_{74}}, $ $ \underline{x_{169}}, x_{145} $
29 $ x_{285}^0 $ $ x_{29}, \overline{x_{70}}, \underline{x_{99}} $ $ x_{281}^1 $ $ x_{281}^0, \overline{x_{71}}, $ $ \underline{x_{112}}, x_{37} $ $ x_{277}^2 $ $ x_{277}^1, \overline{x_{73}}, $ $ \underline{x_{131}}, \overline{x_{69}} $ $ x_{273}^3 $ $ x_{273}^2, \overline{x_{72}}, $ $ \underline{x_{147}}, x_{132} $ $ x_{269}^4 $ $ x_{269}^3, \overline{x_{75}}, $ $ \underline{x_{170}}, x_{146} $
30 $ x_{286}^0 $ $ x_{30}, \overline{x_{71}}, \underline{x_{100}} $ $ x_{282}^1 $ $ x_{282}^0, \overline{x_{72}}, $ $ \underline{x_{113}}, x_{38} $ $ x_{278}^2 $ $ x_{278}^1, \overline{x_{74}}, $ $ \underline{x_{132}}, \overline{x_{70}} $ $ x_{274}^3 $ $ x_{274}^2, \overline{x_{73}}, $ $ \underline{x_{148}}, x_{133} $ $ x_{270}^4 $ $ x_{270}^3, \overline{x_{76}}, $ $ \underline{x_{171}}, x_{147} $
31 $ x_{287}^0 $ $ x_{31}, \overline{x_{72}}, \underline{x_{101}} $ $ x_{283}^1 $ $ x_{283}^0, \overline{x_{73}}, $ $ \underline{x_{114}}, x_{39} $ $ x_{279}^2 $ $ x_{279}^1, \overline{x_{75}}, $ $ \underline{x_{133}}, \overline{x_{71}} $ $ x_{275}^3 $ $ x_{275}^2, \overline{x_{74}}, $ $ \underline{x_{149}}, x_{134} $ $ x_{271}^4 $ $ x_{271}^3, x_{77}, $ $ x_{172}, x_{148} $
32 $ x_{288}^0 $ $ x_{32}, \overline{x_{73}}, \underline{x_{102}} $ $ x_{284}^1 $ $ x_{284}^0, \overline{x_{74}}, $ $ \underline{x_{115}}, x_{40} $ $ x_{280}^2 $ $ x_{280}^1, \overline{x_{76}}, $ $ \underline{x_{134}}, \overline{x_{72}} $ $ x_{276}^3 $ $ x_{276}^2, \overline{x_{75}}, $ $ \underline{x_{150}}, x_{135} $ $ x_{272}^4 $ $ x_{272}^3, x_{78}, $ $ x_{173}, x_{149} $
33 $ x_{289}^0 $ $ x_{33}, \overline{x_{74}}, \underline{x_{103}} $ $ x_{285}^1 $ $ x_{285}^0, \overline{x_{75}}, $ $ \underline{x_{116}}, x_{41} $ $ x_{281}^2 $ $ x_{281}^1, x_{77}, $ $ x_{135}, \overline{x_{73}} $ $ x_{277}^3 $ $ x_{277}^2, \overline{x_{76}}, $ $ \underline{x_{151}}, x_{136} $ $ x_{273}^4 $ $ x_{273}^3, x_{79}, $ $ x_{174}, x_{150} $
34 $ x_{290}^0 $ $ x_{34}, \overline{x_{75}}, \underline{x_{104}} $ $ x_{286}^1 $ $ \underline{x_{286}^0}, \overline{x_{76}}, $ $ \underline{x_{117}}, x_{42} $ $ x_{282}^2 $ $ x_{282}^1, x_{78}, $ $ x_{136}, \overline{x_{74}} $ $ x_{278}^3 $ $ x_{278}^2, x_{77}, $ $ x_{152}, x_{137} $ $ x_{274}^4 $ $ x_{274}^3, x_{80}, $ $ x_{175}, x_{151} $
Row Feedback bit calculaton because of (5) Column 0 Feedback bit calculaton because of (6) Column 1 Feedback bit calculaton because of (7) Column 2 Feedback bit calculaton because of (8) Column 3 Feedback bit calculaton because of (9) Column 4
Feedback bits State bits appeared on RHS of (5) Feedback bits State bits appeared on RHS of (6) Feedback bits State bits appeared on RHS of (7) Feedback bits State bits appeared on RHS of (8) Feedback bits State bits appeared on RHS of (2)
0 $ x_{256}^0 $ $ x_{0}, \underline{x_{41}}, \overline{x_{70}} $ $ x_{252}^1 $ $ x_{252}, x_{42}, $ $ x_{83}, x_{8} $ $ x_{248}^2 $ $ x_{248}, x_{44}, $ $ x_{102}, x_{40} $ $ x_{244}^3 $ $ x_{244}, x_{43}, $ $ x_{118}, x_{103} $ $ x_{240}^4 $ $ x_{240}, \overline{x_{46}}, $ $ \underline{x_{141}}, x_{117} $
1 $ x_{257}^0 $ $ x_{1}, \underline{x_{42}}, \overline{x_{71}} $ $ x_{253}^1 $ $ x_{253}, x_{43}, $ $ x_{84}, x_{9} $ $ x_{249}^2 $ $ x_{249}, x_{45}, $ $ x_{103}, x_{41} $ $ x_{245}^3 $ $ x_{245}, x_{44}, $ $ x_{119}, x_{104} $ $ x_{241}^4 $ $ x_{241}, \overline{x_{47}}, $ $ \underline{x_{142}}, x_{118} $
2 $ x_{258}^0 $ $ x_{2}, \underline{x_{43}}, \overline{x_{72}} $ $ x_{254}^1 $ $ x_{254}, x_{44}, $ $ x_{85}, x_{10} $ $ x_{250}^2 $ $ x_{250}, \overline{x_{46}}, $ $ \underline{x_{104}}, x_{42} $ $ x_{246}^3 $ $ x_{246}, x_{45}, $ $ x_{120}, x_{105} $ $ x_{242}^4 $ $ x_{242}, \overline{x_{48}}, $ $ \underline{x_{143}}, x_{119} $
3 $ x_{259}^0 $ $ x_{3}, \underline{x_{44}}, \overline{x_{73}} $ $ x_{255}^1 $ $ x_{255}, x_{45}, $ $ x_{86}, x_{11} $ $ x_{251}^2 $ $ x_{251}, \overline{x_{47}}, $ $ \underline{x_{105}}, x_{43} $ $ x_{247}^3 $ $ x_{247}, \overline{x_{46}}, $ $ \underline{x_{121}}, x_{106} $ $ x_{243}^4 $ $ x_{243}, \overline{x_{49}}, $ $ \underline{x_{144}}, x_{120} $
4 $ x_{260}^0 $ $ x_{4}, \underline{x_{45}}, \overline{x_{74}} $ $ x_{256}^1 $ $ x_{256}^0, \overline{x_{46}}, $ $ \underline{x_{87}}, x_{12} $ $ x_{252}^2 $ $ x_{252}^1, \overline{x_{48}}, $ $ \underline{x_{106}}, x_{44} $ $ x_{248}^3 $ $ x_{248}^2, \overline{x_{47}}, $ $ \underline{x_{122}}, x_{107} $ $ x_{244}^4 $ $ x_{244}^3, \overline{x_{50}}, $ $ \underline{x_{145}}, x_{121} $
5 $ x_{261}^0 $ $ x_{5}, \overline{x_{46}}, \overline{x_{75}} $ $ x_{257}^1 $ $ x_{257}^0, \overline{x_{47}}, $ $ \underline{x_{88}}, x_{13} $ $ x_{253}^2 $ $ x_{253}^1, \overline{x_{49}}, $ $ \underline{x_{107}}, x_{45} $ $ x_{249}^3 $ $ x_{249}^2, \overline{x_{48}}, $ $ \underline{x_{123}}, x_{108} $ $ x_{245}^4 $ $ x_{245}^3, \overline{x_{51}}, $ $ \underline{x_{146}}, x_{122} $
6 $ x_{262}^0 $ $ x_{6}, \overline{x_{47}}, \overline{x_{76}} $ $ x_{258}^1 $ $ x_{258}^0, \overline{x_{48}}, $ $ \underline{x_{89}}, x_{14} $ $ x_{254}^2 $ $ x_{254}^1, \overline{x_{50}}, $ $ \underline{x_{108}}, \overline{x_{46}} $ $ x_{250}^3 $ $ x_{250}^2, \overline{x_{49}}, $ $ \underline{x_{124}}, x_{109} $ $ x_{246}^4 $ $ x_{246}^3, \overline{x_{52}}, $ $ \underline{x_{147}}, x_{123} $
7 $ x_{263}^0 $ $ x_{7}, \overline{x_{48}}, \underline{x_{77}} $ $ x_{259}^1 $ $ x_{259}^0, \overline{x_{49}}, $ $ \underline{x_{90}}, x_{15} $ $ x_{255}^2 $ $ x_{255}^1, \overline{x_{51}}, $ $ \underline{x_{109}}, \overline{x_{47}} $ $ x_{251}^3 $ $ x_{251}^2, \overline{x_{50}}, $ $ \underline{x_{125}}, x_{110} $ $ x_{247}^4 $ $ x_{247}^3, \overline{x_{53}}, $ $ \underline{x_{148}}, x_{124} $
8 $ x_{264}^0 $ $ x_{8}, \overline{x_{49}}, \underline{x_{78}} $ $ x_{260}^1 $ $ x_{260}^0, \overline{x_{50}}, $ $ \underline{x_{91}}, x_{16} $ $ x_{256}^2 $ $ x_{256}^1, \overline{x_{52}}, $ $ \underline{x_{110}}, \overline{x_{48}} $ $ x_{252}^3 $ $ x_{252}^2, \overline{x_{51}}, $ $ \underline{x_{126}}, x_{111} $ $ x_{248}^4 $ $ x_{248}^3, \overline{x_{54}}, $ $ \underline{x_{149}}, x_{125} $
9 $ x_{265}^0 $ $ x_{9}, \overline{x_{50}}, \underline{x_{79}} $ $ x_{261}^1 $ $ x_{261}^0, \overline{x_{51}}, $ $ \underline{x_{92}}, x_{17} $ $ x_{257}^2 $ $ x_{257}^1, \overline{x_{53}}, $ $ \underline{x_{111}}, \overline{x_{49}} $ $ x_{253}^3 $ $ x_{253}^2, \overline{x_{52}}, $ $ \underline{x_{127}}, x_{112} $ $ x_{249}^4 $ $ x_{249}^3, \overline{x_{55}}, $ $ \underline{x_{150}}, x_{126} $
10 $ x_{266}^0 $ $ x_{10}, \overline{x_{51}}, \underline{x_{80}} $ $ x_{262}^1 $ $ x_{262}^0, \overline{x_{52}}, $ $ \underline{x_{93}}, x_{18} $ $ x_{258}^2 $ $ x_{258}^1, \overline{x_{54}}, $ $ \underline{x_{112}}, \overline{x_{50}} $ $ x_{254}^3 $ $ x_{254}^2, \overline{x_{53}}, $ $ \underline{x_{128}}, x_{113} $ $ x_{250}^4 $ $ x_{250}^3, \overline{x_{56}}, $ $ \underline{x_{151}}, x_{127} $
11 $ x_{267}^0 $ $ x_{11}, \overline{x_{52}}, \underline{x_{81}} $ $ x_{263}^1 $ $ x_{263}^0, \overline{x_{53}}, $ $ \underline{x_{94}}, x_{19} $ $ x_{259}^2 $ $ x_{259}^1, \overline{x_{55}}, $ $ \underline{x_{113}}, \overline{x_{51}} $ $ x_{255}^3 $ $ x_{255}^2, \overline{x_{54}}, $ $ \underline{x_{129}}, x_{114} $ $ x_{251}^4 $ $ x_{251}^3, \overline{x_{57}}, $ $ \underline{x_{152}}, x_{128} $
12 $ x_{268}^0 $ $ x_{12}, \overline{x_{53}}, \underline{x_{82}} $ $ x_{264}^1 $ $ x_{264}^0, \overline{x_{54}}, $ $ \underline{x_{95}}, x_{20} $ $ x_{260}^2 $ $ x_{260}^1, \overline{x_{56}}, $ $ \underline{x_{114}}, \overline{x_{52}} $ $ x_{256}^3 $ $ x_{256}^2, \overline{x_{55}}, $ $ \underline{x_{130}}, x_{115} $ $ x_{252}^4 $ $ x_{252}^3, \overline{x_{58}}, $ $ \underline{x_{153}}, x_{129} $
13 $ x_{269}^0 $ $ x_{13}, \overline{x_{54}}, \underline{x_{83}} $ $ x_{265}^1 $ $ x_{265}^0, \overline{x_{55}}, $ $ \underline{x_{96}}, x_{21} $ $ x_{261}^2 $ $ x_{261}^1, \overline{x_{57}}, $ $ \underline{x_{115}}, \overline{x_{53}} $ $ x_{257}^3 $ $ x_{257}^2, \overline{x_{56}}, $ $ \underline{x_{131}}, x_{116} $ $ x_{253}^4 $ $ x_{253}^3, \overline{x_{59}}, $ $ \underline{x_{154}}, x_{130} $
14 $ x_{270}^0 $ $ x_{14}, \overline{x_{55}}, \underline{x_{84}} $ $ x_{266}^1 $ $ x_{266}^0, \overline{x_{56}}, $ $ \underline{x_{97}}, x_{22} $ $ x_{262}^2 $ $ x_{262}^1, \overline{x_{58}}, $ $ \underline{x_{116}}, \overline{x_{54}} $ $ x_{258}^3 $ $ x_{258}^2, \overline{x_{57}}, $ $ \underline{x_{132}}, x_{117} $ $ x_{254}^4 $ $ x_{254}^3, \overline{x_{60}}, $ $ \underline{x_{155}}, x_{131} $
15 $ x_{271}^0 $ $ x_{15}, \overline{x_{56}}, \underline{x_{85}} $ $ x_{267}^1 $ $ x_{267}^0, \overline{x_{57}}, $ $ \underline{x_{98}}, x_{23} $ $ x_{263}^2 $ $ x_{263}^1, \overline{x_{59}}, $ $ \underline{x_{117}}, \overline{x_{55}} $ $ x_{259}^3 $ $ x_{259}^2, \overline{x_{58}}, $ $ \underline{x_{133}}, x_{118} $ $ x_{255}^4 $ $ x_{255}^3, \overline{x_{61}}, $ $ \underline{x_{156}}, x_{132} $
16 $ x_{272}^0 $ $ x_{16}, \overline{x_{57}}, \underline{x_{86}} $ $ x_{268}^1 $ $ x_{268}^0, \overline{x_{58}}, $ $ \underline{x_{99}}, x_{24} $ $ x_{264}^2 $ $ x_{264}^1, \overline{x_{60}}, $ $ \underline{x_{118}}, \overline{x_{56}} $ $ x_{260}^3 $ $ x_{260}^2, \overline{x_{59}}, $ $ \underline{x_{134}}, x_{119} $ $ x_{256}^4 $ $ x_{256}^3, \overline{x_{62}}, $ $ \underline{x_{157}}, x_{133} $
17 $ x_{273}^0 $ $ x_{17}, \overline{x_{58}}, \underline{x_{87}} $ $ x_{269}^1 $ $ x_{269}^0, \overline{x_{59}}, $ $ \underline{x_{100}}, x_{25} $ $ x_{265}^2 $ $ x_{265}^1, \overline{x_{61}}, $ $ \underline{x_{119}}, \overline{x_{57}} $ $ x_{261}^3 $ $ x_{261}^2, \overline{x_{60}}, $ $ \underline{x_{135}}, x_{120} $ $ x_{257}^4 $ $ x_{257}^3, \overline{x_{63}}, $ $ \underline{x_{158}}, x_{134} $
18 $ x_{274}^0 $ $ x_{18}, \overline{x_{59}}, \underline{x_{88}} $ $ x_{270}^1 $ $ x_{270}^0, \overline{x_{60}}, $ $ \underline{x_{101}}, x_{26} $ $ x_{266}^2 $ $ x_{266}^1, \overline{x_{62}}, $ $ \underline{x_{120}}, \overline{x_{58}} $ $ x_{262}^3 $ $ x_{262}^2, \overline{x_{61}}, $ $ \underline{x_{136}}, x_{121} $ $ x_{258}^4 $ $ x_{258}^3, \overline{x_{64}}, $ $ \underline{x_{159}}, x_{135} $
19 $ x_{275}^0 $ $ x_{19}, \overline{x_{60}}, \underline{x_{89}} $ $ x_{271}^1 $ $ x_{271}^0, \overline{x_{61}}, $ $ \underline{x_{102}}, x_{27} $ $ x_{267}^2 $ $ x_{267}^1, \overline{x_{63}}, $ $ \underline{x_{121}}, \overline{x_{59}} $ $ x_{263}^3 $ $ x_{263}^2, \overline{x_{62}}, $ $ \underline{x_{137}}, x_{122} $ $ x_{259}^4 $ $ x_{259}^3, \overline{x_{65}}, $ $ \underline{x_{160}}, x_{136} $
20 $ x_{276}^0 $ $ x_{20}, \overline{x_{61}}, \underline{x_{90}} $ $ x_{272}^1 $ $ x_{272}^0, \overline{x_{62}}, $ $ \underline{x_{103}}, x_{28} $ $ x_{268}^2 $ $ x_{268}^1, \overline{x_{64}}, $ $ \underline{x_{122}}, \overline{x_{60}} $ $ x_{264}^3 $ $ x_{264}^2, \overline{x_{63}}, $ $ \underline{x_{138}}, x_{123} $ $ x_{260}^4 $ $ x_{260}^3, \overline{x_{66}}, $ $ \underline{x_{161}}, x_{137} $
21 $ x_{277}^0 $ $ x_{21}, \overline{x_{62}}, \underline{x_{91}} $ $ x_{273}^1 $ $ x_{273}^0, \overline{x_{63}}, $ $ \underline{x_{104}}, x_{29} $ $ x_{269}^2 $ $ x_{269}^1, \overline{x_{65}}, $ $ \underline{x_{123}}, \overline{x_{61}} $ $ x_{265}^3 $ $ x_{265}^2, \overline{x_{64}}, $ $ \underline{x_{139}}, x_{124} $ $ x_{261}^4 $ $ x_{261}^3, \overline{x_{67}}, $ $ \underline{x_{162}}, x_{138} $
22 $ x_{278}^0 $ $ x_{22}, \overline{x_{63}}, \underline{x_{92}} $ $ x_{274}^1 $ $ x_{274}^0, \overline{x_{64}}, $ $ \underline{x_{105}}, x_{30} $ $ x_{270}^2 $ $ x_{270}^1, \overline{x_{66}}, $ $ \underline{x_{124}}, \overline{x_{62}} $ $ x_{266}^3 $ $ x_{266}^2, \overline{x_{65}}, $ $ \underline{x_{140}}, x_{125} $ $ x_{262}^4 $ $ x_{262}^3, \overline{x_{68}}, $ $ \underline{x_{163}}, x_{139} $
23 $ x_{279}^0 $ $ x_{23}, \overline{x_{64}}, \underline{x_{93}} $ $ x_{275}^1 $ $ x_{275}^0, \overline{x_{65}}, $ $ \underline{x_{106}}, x_{31} $ $ x_{271}^2 $ $ x_{271}^1, \overline{x_{67}}, $ $ \underline{x_{125}}, \overline{x_{63}} $ $ x_{267}^3 $ $ x_{267}^2, \overline{x_{66}}, $ $ \underline{x_{141}}, x_{126} $ $ x_{263}^4 $ $ x_{263}^3, \overline{x_{69}}, $ $ \underline{x_{164}}, x_{140} $
24 $ x_{280}^0 $ $ x_{24}, \overline{x_{65}}, \underline{x_{94}} $ $ x_{276}^1 $ $ x_{276}^0, \overline{x_{66}}, $ $ \underline{x_{107}}, x_{32} $ $ x_{272}^2 $ $ x_{272}^1, \overline{x_{68}}, $ $ \underline{x_{126}}, \overline{x_{64}} $ $ x_{268}^3 $ $ x_{268}^2, \overline{x_{67}}, $ $ \underline{x_{142}}, x_{127} $ $ x_{264}^4 $ $ x_{264}^3, \overline{x_{70}}, $ $ \underline{x_{165}}, x_{141} $
25 $ x_{281}^0 $ $ x_{25}, \overline{x_{66}}, \underline{x_{95}} $ $ x_{277}^1 $ $ x_{277}^0, \overline{x_{67}}, $ $ \underline{x_{108}}, x_{33} $ $ x_{273}^2 $ $ x_{273}^1, \overline{x_{69}}, $ $ \underline{x_{127}}, \overline{x_{65}} $ $ x_{269}^3 $ $ x_{269}^2, \overline{x_{68}}, $ $ \underline{x_{143}}, x_{128} $ $ x_{265}^4 $ $ x_{265}^3, \overline{x_{71}}, $ $ \underline{x_{166}}, x_{142} $
26 $ x_{282}^0 $ $ x_{26}, \overline{x_{67}}, \underline{x_{96}} $ $ x_{278}^1 $ $ x_{278}^0, \overline{x_{68}}, $ $ \underline{x_{109}}, x_{34} $ $ x_{274}^2 $ $ x_{274}^1, \overline{x_{70}}, $ $ \underline{x_{128}}, \overline{x_{66}} $ $ x_{270}^3 $ $ x_{270}^2, \overline{x_{69}}, $ $ \underline{x_{144}}, x_{129} $ $ x_{266}^4 $ $ x_{266}^3, \overline{x_{72}}, $ $ \underline{x_{167}}, x_{143} $
27 $ x_{283}^0 $ $ x_{27}, \overline{x_{68}}, \underline{x_{97}} $ $ x_{279}^1 $ $ x_{279}^0, \overline{x_{69}}, $ $ \underline{x_{110}}, x_{35} $ $ x_{275}^2 $ $ x_{275}^1, \overline{x_{71}}, $ $ \underline{x_{129}}, \overline{x_{67}} $ $ x_{271}^3 $ $ x_{271}^2, \overline{x_{70}}, $ $ \underline{x_{145}}, x_{130} $ $ x_{267}^4 $ $ x_{267}^3, \overline{x_{73}}, $ $ \underline{x_{168}}, x_{144} $
28 $ x_{284}^0 $ $ x_{28}, \overline{x_{69}}, \underline{x_{98}} $ $ x_{280}^1 $ $ x_{280}^0, \overline{x_{70}}, $ $ \underline{x_{111}}, x_{36} $ $ x_{276}^2 $ $ x_{276}^1, \overline{x_{72}}, $ $ \underline{x_{130}}, \overline{x_{68}} $ $ x_{272}^3 $ $ x_{272}^2, \overline{x_{71}}, $ $ \underline{x_{146}}, x_{131} $ $ x_{268}^4 $ $ x_{268}^3, \overline{x_{74}}, $ $ \underline{x_{169}}, x_{145} $
29 $ x_{285}^0 $ $ x_{29}, \overline{x_{70}}, \underline{x_{99}} $ $ x_{281}^1 $ $ x_{281}^0, \overline{x_{71}}, $ $ \underline{x_{112}}, x_{37} $ $ x_{277}^2 $ $ x_{277}^1, \overline{x_{73}}, $ $ \underline{x_{131}}, \overline{x_{69}} $ $ x_{273}^3 $ $ x_{273}^2, \overline{x_{72}}, $ $ \underline{x_{147}}, x_{132} $ $ x_{269}^4 $ $ x_{269}^3, \overline{x_{75}}, $ $ \underline{x_{170}}, x_{146} $
30 $ x_{286}^0 $ $ x_{30}, \overline{x_{71}}, \underline{x_{100}} $ $ x_{282}^1 $ $ x_{282}^0, \overline{x_{72}}, $ $ \underline{x_{113}}, x_{38} $ $ x_{278}^2 $ $ x_{278}^1, \overline{x_{74}}, $ $ \underline{x_{132}}, \overline{x_{70}} $ $ x_{274}^3 $ $ x_{274}^2, \overline{x_{73}}, $ $ \underline{x_{148}}, x_{133} $ $ x_{270}^4 $ $ x_{270}^3, \overline{x_{76}}, $ $ \underline{x_{171}}, x_{147} $
31 $ x_{287}^0 $ $ x_{31}, \overline{x_{72}}, \underline{x_{101}} $ $ x_{283}^1 $ $ x_{283}^0, \overline{x_{73}}, $ $ \underline{x_{114}}, x_{39} $ $ x_{279}^2 $ $ x_{279}^1, \overline{x_{75}}, $ $ \underline{x_{133}}, \overline{x_{71}} $ $ x_{275}^3 $ $ x_{275}^2, \overline{x_{74}}, $ $ \underline{x_{149}}, x_{134} $ $ x_{271}^4 $ $ x_{271}^3, x_{77}, $ $ x_{172}, x_{148} $
32 $ x_{288}^0 $ $ x_{32}, \overline{x_{73}}, \underline{x_{102}} $ $ x_{284}^1 $ $ x_{284}^0, \overline{x_{74}}, $ $ \underline{x_{115}}, x_{40} $ $ x_{280}^2 $ $ x_{280}^1, \overline{x_{76}}, $ $ \underline{x_{134}}, \overline{x_{72}} $ $ x_{276}^3 $ $ x_{276}^2, \overline{x_{75}}, $ $ \underline{x_{150}}, x_{135} $ $ x_{272}^4 $ $ x_{272}^3, x_{78}, $ $ x_{173}, x_{149} $
33 $ x_{289}^0 $ $ x_{33}, \overline{x_{74}}, \underline{x_{103}} $ $ x_{285}^1 $ $ x_{285}^0, \overline{x_{75}}, $ $ \underline{x_{116}}, x_{41} $ $ x_{281}^2 $ $ x_{281}^1, x_{77}, $ $ x_{135}, \overline{x_{73}} $ $ x_{277}^3 $ $ x_{277}^2, \overline{x_{76}}, $ $ \underline{x_{151}}, x_{136} $ $ x_{273}^4 $ $ x_{273}^3, x_{79}, $ $ x_{174}, x_{150} $
34 $ x_{290}^0 $ $ x_{34}, \overline{x_{75}}, \underline{x_{104}} $ $ x_{286}^1 $ $ \underline{x_{286}^0}, \overline{x_{76}}, $ $ \underline{x_{117}}, x_{42} $ $ x_{282}^2 $ $ x_{282}^1, x_{78}, $ $ x_{136}, \overline{x_{74}} $ $ x_{278}^3 $ $ x_{278}^2, x_{77}, $ $ x_{152}, x_{137} $ $ x_{274}^4 $ $ x_{274}^3, x_{80}, $ $ x_{175}, x_{151} $
Table 2.  State Bits required to calculate feedback bits
Row Feedback bit calculaton because of (10) Column 5 Feedback bit calculaton because of (11) Column 6 Feedback bit calculaton because of (12) Column 7 Feedback bit calculaton because of (13) Column 8 Feedback bit calculaton because of (14) Column 9
Feedback bits State bits appeared on RHS of (10) Feedback bits State bits appeared on RHS of (11) Feedback bits State bits appeared on RHS of (12) Feedback bits State bits appeared on RHS of (13) Feedback bits State bits appeared on RHS of (14)
0 $ x_{236}^5 $ $ x_{236}, \overline{x_{67}}, \underline{x_{90}, x_{110}, x_{137}} $ $ x_{232}^6 $ $ x_{232}, \overline{x_{50}}, $ $ \underline{x_{159}}, x_{189} $ $ x_{218}^7 $ $ x_{218}, \underline{x_{3}}, \overline{x_{32}} $ $ x_{214}^8 $ $ x_{214}, x_{4}, x_{45} $ $ x_{210}^9 $ $ x_{210}, \underline{x_{6}}, \overline{x_{64}} $
1 $ x_{237}^5 $ $ x_{237}, \overline{x_{68}}, \underline{x_{91}, x_{111}, x_{138}} $ $ x_{233}^6 $ $ x_{233}, \overline{x_{51}}, $ $ \underline{x_{160}}, x_{190} $ $ x_{219}^7 $ $ x_{219}, \underline{x_{4}}, \overline{x_{33}} $ $ x_{215}^8 $ $ x_{215}, \underline{x_{5}}, \overline{x_{46}} $ $ x_{211}^9 $ $ x_{211}, \underline{x_{7}}, \overline{x_{65}} $
2 $ x_{238}^5 $ $ x_{238}, \overline{x_{69}}, \underline{x_{92}, x_{112}, x_{139}} $ $ x_{234}^6 $ $ x_{234}, \overline{x_{52}}, $ $ \underline{x_{161}}, x_{191} $ $ x_{220}^7 $ $ x_{220}, \underline{x_{5}}, \overline{x_{34}} $ $ x_{216}^8 $ $ x_{216}, \underline{x_{6}}, \overline{x_{47}} $ $ x_{212}^9 $ $ x_{212}, \underline{x_{8}}, \overline{x_{66}} $
3 $ x_{239}^5 $ $ x_{239}, \overline{x_{70}}, \underline{x_{93}, x_{113}, x_{140}} $ $ x_{235}^6 $ $ x_{235}, \overline{x_{53}}, $ $ \underline{x_{162}}, x_{192} $ $ x_{221}^7 $ $ x_{221}, \underline{x_{6}}, \overline{x_{35}} $ $ x_{217}^8 $ $ x_{217}, \underline{x_{7}}, \overline{x_{48}} $ $ x_{213}^9 $ $ x_{213}, \underline{x_{9}}, \overline{x_{67}} $
4 $ x_{240}^5 $ $ x_{240}^4, \overline{x_{71}}, \underline{x_{94}, x_{114}, x_{141}} $ $ x_{236}^6 $ $ x_{236}^5, \overline{x_{54}}, $ $ \underline{x_{163}}, x_{193} $ $ x_{222}^7 $ $ x_{222}, \underline{x_{7}}, \overline{x_{36}} $ $ x_{218}^8 $ $ x_{218}^7, \underline{x_{8}}, \overline{x_{49}} $ $ x_{214}^9 $ $ x_{214}^8, \underline{x_{10}}, \overline{x_{68}} $
5 $ x_{241}^5 $ $ x_{241}^4, \overline{x_{72}}, \underline{x_{95}, x_{115}, x_{142}} $ $ x_{237}^6 $ $ x_{237}^5, \overline{x_{55}}, $ $ \underline{x_{164}}, x_{194}^{13} $ $ x_{223}^7 $ $ x_{223}, x_{8}, x_{37} $ $ x_{219}^8 $ $ x_{219}^7, \underline{x_{9}}, \overline{x_{50}} $ $ x_{215}^9 $ $ x_{215}^8, \underline{x_{11}}, \overline{x_{69}} $
6 $ x_{242}^5 $ $ x_{242}^4, \overline{x_{73}}, \underline{x_{96}, x_{116}, x_{143}} $ $ x_{238}^6 $ $ x_{238}^5, \overline{x_{56}}, $ $ \underline{x_{165}}, x_{195}^{13} $ $ x_{224}^7 $ $ x_{224}, x_{9}, x_{38} $ $ x_{220}^8 $ $ x_{220}^7, \underline{x_{10}}, \overline{x_{51}} $ $ x_{216}^9 $ $ x_{216}^8, \underline{x_{12}}, \overline{x_{70}} $
7 $ x_{243}^5 $ $ x_{243}^4, \overline{x_{74}}, \underline{x_{97}, x_{117}, x_{144}} $ $ x_{239}^6 $ $ x_{239}^5, \overline{x_{57}}, $ $ \underline{x_{166}}, x_{196}^{13} $ $ x_{225}^7 $ $ x_{225}, x_{10}, x_{39} $ $ x_{221}^8 $ $ x_{221}^7, \underline{x_{11}}, \overline{x_{52}} $ $ x_{217}^9 $ $ x_{217}^8, \underline{x_{13}}, \overline{x_{71}} $
8 $ x_{244}^5 $ $ x_{244}^4, \overline{x_{75}}, \underline{x_{98}, x_{118}, x_{145}} $ $ x_{240}^6 $ $ x_{240}^5, \overline{x_{58}}, $ $ \underline{x_{167}}, x_{197}^{13} $ $ x_{226}^7 $ $ x_{226}, x_{11}, x_{40} $ $ x_{222}^8 $ $ x_{222}^7, \underline{x_{12}}, \overline{x_{53}} $ $ x_{218}^9 $ $ x_{218}^8, \underline{x_{14}}, \overline{x_{72}} $
9 $ x_{245}^5 $ $ x_{245}^4, \overline{x_{76}}, \underline{x_{99}, x_{119}, x_{146}} $ $ x_{241}^6 $ $ x_{241}^5, \overline{x_{59}}, $ $ \underline{x_{168}}, x_{198}^{13} $ $ x_{227}^7 $ $ x_{227}, x_{12}, x_{41} $ $ x_{223}^8 $ $ x_{223}^7, \underline{x_{13}}, \overline{x_{54}} $ $ x_{219}^9 $ $ x_{219}^8, \underline{x_{15}}, \overline{x_{73}} $
10 $ x_{246}^5 $ $ x_{246}^4, x_{77}, x_{100}, x_{120}, x_{147} $ $ x_{242}^6 $ $ x_{242}^5, \overline{x_{60}}, $ $ \underline{x_{169}}, x_{199}^{13} $ $ x_{228}^7 $ $ x_{228}, x_{13}, x_{42} $ $ x_{224}^8 $ $ x_{224}^7, \underline{x_{14}}, \overline{x_{55}} $ $ x_{220}^9 $ $ x_{220}^8, \underline{x_{16}}, \overline{x_{74}} $
11 $ x_{247}^5 $ $ x_{247}^4, x_{78}, x_{101}, x_{121}, x_{148} $ $ x_{243}^6 $ $ x_{243}^5, \overline{x_{61}}, $ $ \underline{x_{170}}, x_{200}^{13} $ $ x_{229}^7 $ $ x_{229}, x_{14}, x_{43} $ $ x_{225}^8 $ $ x_{225}^7, \underline{x_{15}}, \overline{x_{56}} $ $ x_{221}^9 $ $ x_{221}^8, \underline{x_{17}}, \overline{x_{75}} $
12 $ x_{248}^5 $ $ x_{248}^4, x_{79}, x_{102}, x_{122}, x_{149} $ $ x_{244}^6 $ $ x_{244}^5, \overline{x_{62}}, $ $ \underline{x_{171}}, x_{201}^{13} $ $ x_{230}^7 $ $ x_{230}, x_{15}, x_{44} $ $ x_{226}^8 $ $ x_{226}^7, \underline{x_{16}}, \overline{x_{57}} $ $ x_{222}^9 $ $ x_{222}^8, \underline{x_{18}}, \overline{x_{76}} $
13 $ x_{249}^5 $ $ x_{249}^4, x_{80}, x_{103}, x_{123}, x_{150} $ $ x_{245}^6 $ $ x_{245}^5, \overline{x_{63}}, $ $ \underline{x_{172}}, x_{202}^{13} $ $ x_{231}^7 $ $ x_{231}, x_{16}, x_{45} $ $ x_{227}^8 $ $ x_{227}^7, \underline{x_{17}}, \overline{x_{58}} $ $ x_{223}^9 $ $ x_{223}^8, x_{19}, x_{77} $
14 $ x_{250}^5 $ $ x_{250}^4, x_{81}, x_{104}, x_{124}, x_{151} $ $ x_{246}^6 $ $ x_{246}^5, \overline{x_{64}}, $ $ \underline{x_{173}}, x_{203}^{13} $ $ x_{232}^7 $ $ x_{232}^6, \underline{x_{17}}, \overline{x_{46}} $ $ x_{228}^8 $ $ x_{228}^7, \underline{x_{18}}, \overline{x_{59}} $ $ x_{224}^9 $ $ x_{224}^8, x_{20}, x_{78} $
15 $ x_{251}^5 $ $ x_{251}^4, x_{82}, x_{105}, x_{125}, x_{152} $ $ x_{247}^6 $ $ x_{247}^5, \overline{x_{65}}, $ $ \underline{x_{174}}, x_{204}^{13} $ $ x_{233}^7 $ $ x_{233}^6, \underline{x_{18}}, \overline{x_{47}} $ $ x_{229}^8 $ $ x_{229}^7, \underline{x_{19}}, \overline{x_{60}} $ $ x_{225}^9 $ $ x_{225}^8, x_{21}, x_{79} $
16 $ x_{252}^5 $ $ x_{252}^4, x_{83}, x_{106}, x_{126}, x_{153} $ $ x_{248}^6 $ $ x_{248}^5, \overline{x_{66}}, $ $ \underline{x_{175}}, x_{205}^{13} $ $ x_{234}^7 $ $ x_{234}^6, \underline{x_{19}}, \overline{x_{48}} $ $ x_{230}^8 $ $ x_{230}^7, \underline{x_{20}}, \overline{x_{61}} $ $ x_{226}^9 $ $ x_{226}^8, x_{22}, x_{80} $
17 $ x_{253}^5 $ $ x_{253}^4, x_{84}, x_{107}, x_{127}, x_{154} $ $ x_{249}^6 $ $ x_{249}^5, \overline{x_{67}}, $ $ \underline{x_{176}}, x_{206}^{13} $ $ x_{235}^7 $ $ x_{235}^6, \underline{x_{20}}, \overline{x_{49}} $ $ x_{231}^8 $ $ x_{231}^7, \underline{x_{21}}, \overline{x_{62}} $ $ x_{227}^9 $ $ x_{227}^8, x_{23}, x_{81} $
18 $ x_{254}^5 $ $ x_{254}^4, x_{85}, x_{108}, x_{128}, x_{155} $ $ x_{250}^6 $ $ x_{250}^5, \overline{x_{68}}, $ $ \underline{x_{177}}, x_{207}^{13} $ $ x_{236}^7 $ $ x_{236}^6, \underline{x_{21}}, \overline{x_{50}} $ $ x_{232}^8 $ $ x_{232}^7, \underline{x_{22}}, \overline{x_{63}} $ $ x_{228}^9 $ $ x_{228}^8, x_{24}, x_{82} $
19 $ x_{255}^5 $ $ x_{255}^4, x_{86}, x_{109}, x_{129}, x_{156} $ $ x_{251}^6 $ $ x_{251}^5, \overline{x_{69}}, $ $ \underline{x_{178}}, x_{208}^{13} $ $ x_{237}^7 $ $ x_{237}^6, \underline{x_{22}}, \overline{x_{51}} $ $ x_{233}^8 $ $ x_{233}^7, \underline{x_{23}}, \overline{x_{64}} $ $ x_{229}^9 $ $ x_{229}^8, x_{25}, x_{83} $
20 $ x_{256}^5 $ $ x_{256}^4, x_{87}, x_{110}, x_{130}, x_{157} $ $ x_{252}^6 $ $ x_{252}^5, \overline{x_{70}}, $ $ \underline{x_{179}}, x_{209}^{13} $ $ x_{238}^7 $ $ x_{238}^6, \underline{x_{23}}, \overline{x_{52}} $ $ x_{234}^8 $ $ x_{234}^7, \underline{x_{24}}, \overline{x_{65}} $ $ x_{230}^9 $ $ x_{230}^8, x_{26}, x_{84} $
21 $ x_{257}^5 $ $ x_{257}^4, x_{88}, x_{111}, x_{131}, x_{158} $ $ x_{253}^6 $ $ x_{253}^5, \overline{x_{71}}, $ $ \underline{x_{180}}, x_{210}^{13} $ $ x_{239}^7 $ $ x_{239}^6, \underline{x_{24}}, \overline{x_{53}} $ $ x_{235}^8 $ $ x_{235}^7, \underline{x_{25}}, \overline{x_{66}} $ $ x_{231}^9 $ $ x_{231}^8, x_{27}, x_{85} $
22 $ x_{258}^5 $ $ x_{258}^4, x_{89}, x_{112}, x_{132}, x_{159} $ $ x_{254}^6 $ $ x_{254}^5, \overline{x_{72}}, $ $ \underline{x_{181}}, x_{211}^{13} $ $ x_{240}^7 $ $ x_{240}^6, \underline{x_{25}}, \overline{x_{54}} $ $ x_{236}^8 $ $ x_{236}^7, \underline{x_{26}}, \overline{x_{67}} $ $ x_{232}^9 $ $ x_{232}^8, x_{28}, x_{86} $
23 $ x_{259}^5 $ $ x_{259}^4, x_{90}, x_{113}, x_{133}, x_{160} $ $ x_{255}^6 $ $ x_{255}^5, \overline{x_{73}}, $ $ \underline{x_{182}}, x_{212}^{13} $ $ x_{241}^7 $ $ x_{241}^6, \underline{x_{26}}, \overline{x_{55}} $ $ x_{237}^8 $ $ x_{237}^7, \underline{x_{27}}, \overline{x_{68}} $ $ x_{233}^9 $ $ x_{233}^8, \overline{x_{29}}, \underline{x_{87}} $
24 $ x_{260}^5 $ $ x_{260}^4, x_{91}, x_{114}, x_{134}, x_{161} $ $ x_{256}^6 $ $ x_{256}^5, \overline{x_{74}}, $ $ \underline{x_{183}}, x_{213}^{13} $ $ x_{242}^7 $ $ x_{242}^6, \underline{x_{27}}, \overline{x_{56}} $ $ x_{238}^8 $ $ x_{238}^7, \underline{x_{28}}, \overline{x_{69}} $ $ x_{234}^9 $ $ x_{234}^8, \overline{x_{30}}, \underline{x_{88}} $
25 $ x_{261}^5 $ $ x_{261}^4, x_{92}, x_{115}, x_{135}, x_{162} $ $ x_{257}^6 $ $ x_{257}^5, \overline{x_{75}}, $ $ \underline{x_{184}}, x_{214}^{13} $ $ x_{243}^7 $ $ x_{243}^6, \underline{x_{28}}, \overline{x_{57}} $ $ x_{239}^8 $ $ x_{239}^7, \overline{x_{29}}, \overline{x_{70}} $ $ x_{235}^9 $ $ x_{235}^8, \overline{x_{31}}, \underline{x_{89}} $
26 $ x_{262}^5 $ $ x_{262}^4, x_{93}, x_{116}, x_{136}, x_{163} $ $ x_{258}^6 $ $ x_{258}^5, \overline{x_{76}}, $ $ \underline{x_{185}}, x_{215}^{13} $ $ x_{244}^7 $ $ x_{244}^6, \overline{x_{29}}, \overline{x_{58}} $ $ x_{240}^8 $ $ x_{240}^7, \overline{x_{30}}, \overline{x_{71}} $ $ x_{236}^9 $ $ x_{236}^8, \overline{x_{32}}, \underline{x_{90}} $
27 $ x_{263}^5 $ $ x_{263}^4, x_{94}, x_{117}, x_{137}, x_{164} $ $ x_{259}^6 $ $ x_{259}^5, x_{77}, $ $ x_{186}, x_{216}^{13} $ $ x_{245}^7 $ $ x_{245}^6, \overline{x_{30}}, \overline{x_{59}} $ $ x_{241}^8 $ $ x_{241}^7, \overline{x_{31}}, \overline{x_{72}} $ $ x_{237}^9 $ $ x_{237}^8, \overline{x_{33}}, \underline{x_{91}} $
28 $ x_{264}^5 $ $ x_{264}^4, x_{95}, x_{118}, x_{138}, x_{165} $ $ x_{260}^6 $ $ x_{260}^5, x_{78}, $ $ x_{187}, x_{217}^{13} $ $ x_{246}^7 $ $ x_{246}^6, \overline{x_{31}}, \overline{x_{60}} $ $ x_{242}^8 $ $ x_{242}^7, \overline{x_{32}}, \overline{x_{73}} $ $ x_{238}^9 $ $ x_{238}^8, \overline{x_{34}}, \underline{x_{92}} $
29 $ x_{265}^5 $ $ x_{265}^4, x_{96}, x_{119}, x_{139}, x_{166} $ $ x_{261}^6 $ $ x_{261}^5, x_{79}, $ $ x_{188}, x_{218}^{13} $ $ x_{247}^7 $ $ x_{247}^6, \overline{x_{32}}, \overline{x_{61}} $ $ x_{243}^8 $ $ x_{243}^7, \overline{x_{33}}, \overline{x_{74}} $ $ x_{239}^9 $ $ x_{239}^8, \overline{x_{35}}, \underline{x_{93}} $
30 $ x_{266}^5 $ $ x_{266}^4, x_{97}, x_{120}, x_{140}, x_{167} $ $ x_{262}^6 $ $ x_{262}^5, x_{80}, $ $ x_{189}, x_{219}^{13} $ $ x_{248}^7 $ $ x_{248}^6, \overline{x_{33}}, \overline{x_{62}} $ $ x_{244}^8 $ $ x_{244}^7, \overline{x_{34}}, \overline{x_{75}} $ $ x_{240}^9 $ $ x_{240}^8, \overline{x_{36}}, \underline{x_{94}} $
31 $ x_{267}^5 $ $ x_{267}^4, x_{98}, x_{121}, x_{141}, x_{168} $ $ x_{263}^6 $ $ x_{263}^5, x_{81}, $ $ x_{190}, x_{220}^{13} $ $ x_{249}^7 $ $ x_{249}^6, \overline{x_{34}}, \overline{x_{63}} $ $ x_{245}^8 $ $ x_{245}^7, \overline{x_{35}}, \overline{x_{76}} $ $ x_{241}^9 $ $ x_{241}^8, x_{37}, x_{95} $
32 $ x_{268}^5 $ $ x_{268}^4, x_{99}, x_{122}, x_{142}, x_{169} $ $ x_{264}^6 $ $ x_{264}^5, x_{82}, $ $ x_{191}, x_{221}^{13} $ $ x_{250}^7 $ $ x_{250}^6, \overline{x_{35}}, \overline{x_{64}} $ $ x_{246}^8 $ $ x_{246}^7, \overline{x_{36}},\underline{x_{77}} $ $ x_{242}^9 $ $ x_{242}^8, x_{38}, x_{96} $
33 $ x_{269}^5 $ $ x_{269}^4, x_{100}, x_{123}, x_{143}, x_{170} $ $ x_{265}^6 $ $ x_{265}^5, x_{83}, $ $ x_{192}, x_{222}^{13} $ $ x_{251}^7 $ $ x_{251}^6, \overline{x_{36}}, \overline{x_{65}} $ $ x_{247}^8 $ $ x_{247}^7, x_{37}, x_{78} $ $ x_{243}^9 $ $ x_{243}^8, x_{39}, x_{97} $
34 $ x_{270}^5 $ $ x_{270}^4, x_{101}, x_{124}, x_{144}, x_{171} $ $ x_{266}^6 $ $ x_{266}^5, x_{84}, $ $ x_{193}, x_{223}^{13} $ $ x_{252}^7 $ $ x_{252}^6, \underline{x_{37}}, \overline{x_{66}} $ $ x_{248}^8 $ $ x_{248}^7, x_{38}, x_{79} $ $ x_{244}^9 $ $ x_{244}^8, x_{40}, x_{98} $
Row Feedback bit calculaton because of (10) Column 5 Feedback bit calculaton because of (11) Column 6 Feedback bit calculaton because of (12) Column 7 Feedback bit calculaton because of (13) Column 8 Feedback bit calculaton because of (14) Column 9
Feedback bits State bits appeared on RHS of (10) Feedback bits State bits appeared on RHS of (11) Feedback bits State bits appeared on RHS of (12) Feedback bits State bits appeared on RHS of (13) Feedback bits State bits appeared on RHS of (14)
0 $ x_{236}^5 $ $ x_{236}, \overline{x_{67}}, \underline{x_{90}, x_{110}, x_{137}} $ $ x_{232}^6 $ $ x_{232}, \overline{x_{50}}, $ $ \underline{x_{159}}, x_{189} $ $ x_{218}^7 $ $ x_{218}, \underline{x_{3}}, \overline{x_{32}} $ $ x_{214}^8 $ $ x_{214}, x_{4}, x_{45} $ $ x_{210}^9 $ $ x_{210}, \underline{x_{6}}, \overline{x_{64}} $
1 $ x_{237}^5 $ $ x_{237}, \overline{x_{68}}, \underline{x_{91}, x_{111}, x_{138}} $ $ x_{233}^6 $ $ x_{233}, \overline{x_{51}}, $ $ \underline{x_{160}}, x_{190} $ $ x_{219}^7 $ $ x_{219}, \underline{x_{4}}, \overline{x_{33}} $ $ x_{215}^8 $ $ x_{215}, \underline{x_{5}}, \overline{x_{46}} $ $ x_{211}^9 $ $ x_{211}, \underline{x_{7}}, \overline{x_{65}} $
2 $ x_{238}^5 $ $ x_{238}, \overline{x_{69}}, \underline{x_{92}, x_{112}, x_{139}} $ $ x_{234}^6 $ $ x_{234}, \overline{x_{52}}, $ $ \underline{x_{161}}, x_{191} $ $ x_{220}^7 $ $ x_{220}, \underline{x_{5}}, \overline{x_{34}} $ $ x_{216}^8 $ $ x_{216}, \underline{x_{6}}, \overline{x_{47}} $ $ x_{212}^9 $ $ x_{212}, \underline{x_{8}}, \overline{x_{66}} $
3 $ x_{239}^5 $ $ x_{239}, \overline{x_{70}}, \underline{x_{93}, x_{113}, x_{140}} $ $ x_{235}^6 $ $ x_{235}, \overline{x_{53}}, $ $ \underline{x_{162}}, x_{192} $ $ x_{221}^7 $ $ x_{221}, \underline{x_{6}}, \overline{x_{35}} $ $ x_{217}^8 $ $ x_{217}, \underline{x_{7}}, \overline{x_{48}} $ $ x_{213}^9 $ $ x_{213}, \underline{x_{9}}, \overline{x_{67}} $
4 $ x_{240}^5 $ $ x_{240}^4, \overline{x_{71}}, \underline{x_{94}, x_{114}, x_{141}} $ $ x_{236}^6 $ $ x_{236}^5, \overline{x_{54}}, $ $ \underline{x_{163}}, x_{193} $ $ x_{222}^7 $ $ x_{222}, \underline{x_{7}}, \overline{x_{36}} $ $ x_{218}^8 $ $ x_{218}^7, \underline{x_{8}}, \overline{x_{49}} $ $ x_{214}^9 $ $ x_{214}^8, \underline{x_{10}}, \overline{x_{68}} $
5 $ x_{241}^5 $ $ x_{241}^4, \overline{x_{72}}, \underline{x_{95}, x_{115}, x_{142}} $ $ x_{237}^6 $ $ x_{237}^5, \overline{x_{55}}, $ $ \underline{x_{164}}, x_{194}^{13} $ $ x_{223}^7 $ $ x_{223}, x_{8}, x_{37} $ $ x_{219}^8 $ $ x_{219}^7, \underline{x_{9}}, \overline{x_{50}} $ $ x_{215}^9 $ $ x_{215}^8, \underline{x_{11}}, \overline{x_{69}} $
6 $ x_{242}^5 $ $ x_{242}^4, \overline{x_{73}}, \underline{x_{96}, x_{116}, x_{143}} $ $ x_{238}^6 $ $ x_{238}^5, \overline{x_{56}}, $ $ \underline{x_{165}}, x_{195}^{13} $ $ x_{224}^7 $ $ x_{224}, x_{9}, x_{38} $ $ x_{220}^8 $ $ x_{220}^7, \underline{x_{10}}, \overline{x_{51}} $ $ x_{216}^9 $ $ x_{216}^8, \underline{x_{12}}, \overline{x_{70}} $
7 $ x_{243}^5 $ $ x_{243}^4, \overline{x_{74}}, \underline{x_{97}, x_{117}, x_{144}} $ $ x_{239}^6 $ $ x_{239}^5, \overline{x_{57}}, $ $ \underline{x_{166}}, x_{196}^{13} $ $ x_{225}^7 $ $ x_{225}, x_{10}, x_{39} $ $ x_{221}^8 $ $ x_{221}^7, \underline{x_{11}}, \overline{x_{52}} $ $ x_{217}^9 $ $ x_{217}^8, \underline{x_{13}}, \overline{x_{71}} $
8 $ x_{244}^5 $ $ x_{244}^4, \overline{x_{75}}, \underline{x_{98}, x_{118}, x_{145}} $ $ x_{240}^6 $ $ x_{240}^5, \overline{x_{58}}, $ $ \underline{x_{167}}, x_{197}^{13} $ $ x_{226}^7 $ $ x_{226}, x_{11}, x_{40} $ $ x_{222}^8 $ $ x_{222}^7, \underline{x_{12}}, \overline{x_{53}} $ $ x_{218}^9 $ $ x_{218}^8, \underline{x_{14}}, \overline{x_{72}} $
9 $ x_{245}^5 $ $ x_{245}^4, \overline{x_{76}}, \underline{x_{99}, x_{119}, x_{146}} $ $ x_{241}^6 $ $ x_{241}^5, \overline{x_{59}}, $ $ \underline{x_{168}}, x_{198}^{13} $ $ x_{227}^7 $ $ x_{227}, x_{12}, x_{41} $ $ x_{223}^8 $ $ x_{223}^7, \underline{x_{13}}, \overline{x_{54}} $ $ x_{219}^9 $ $ x_{219}^8, \underline{x_{15}}, \overline{x_{73}} $
10 $ x_{246}^5 $ $ x_{246}^4, x_{77}, x_{100}, x_{120}, x_{147} $ $ x_{242}^6 $ $ x_{242}^5, \overline{x_{60}}, $ $ \underline{x_{169}}, x_{199}^{13} $ $ x_{228}^7 $ $ x_{228}, x_{13}, x_{42} $ $ x_{224}^8 $ $ x_{224}^7, \underline{x_{14}}, \overline{x_{55}} $ $ x_{220}^9 $ $ x_{220}^8, \underline{x_{16}}, \overline{x_{74}} $
11 $ x_{247}^5 $ $ x_{247}^4, x_{78}, x_{101}, x_{121}, x_{148} $ $ x_{243}^6 $ $ x_{243}^5, \overline{x_{61}}, $ $ \underline{x_{170}}, x_{200}^{13} $ $ x_{229}^7 $ $ x_{229}, x_{14}, x_{43} $ $ x_{225}^8 $ $ x_{225}^7, \underline{x_{15}}, \overline{x_{56}} $ $ x_{221}^9 $ $ x_{221}^8, \underline{x_{17}}, \overline{x_{75}} $
12 $ x_{248}^5 $ $ x_{248}^4, x_{79}, x_{102}, x_{122}, x_{149} $ $ x_{244}^6 $ $ x_{244}^5, \overline{x_{62}}, $ $ \underline{x_{171}}, x_{201}^{13} $ $ x_{230}^7 $ $ x_{230}, x_{15}, x_{44} $ $ x_{226}^8 $ $ x_{226}^7, \underline{x_{16}}, \overline{x_{57}} $ $ x_{222}^9 $ $ x_{222}^8, \underline{x_{18}}, \overline{x_{76}} $
13 $ x_{249}^5 $ $ x_{249}^4, x_{80}, x_{103}, x_{123}, x_{150} $ $ x_{245}^6 $ $ x_{245}^5, \overline{x_{63}}, $ $ \underline{x_{172}}, x_{202}^{13} $ $ x_{231}^7 $ $ x_{231}, x_{16}, x_{45} $ $ x_{227}^8 $ $ x_{227}^7, \underline{x_{17}}, \overline{x_{58}} $ $ x_{223}^9 $ $ x_{223}^8, x_{19}, x_{77} $
14 $ x_{250}^5 $ $ x_{250}^4, x_{81}, x_{104}, x_{124}, x_{151} $ $ x_{246}^6 $ $ x_{246}^5, \overline{x_{64}}, $ $ \underline{x_{173}}, x_{203}^{13} $ $ x_{232}^7 $ $ x_{232}^6, \underline{x_{17}}, \overline{x_{46}} $ $ x_{228}^8 $ $ x_{228}^7, \underline{x_{18}}, \overline{x_{59}} $ $ x_{224}^9 $ $ x_{224}^8, x_{20}, x_{78} $
15 $ x_{251}^5 $ $ x_{251}^4, x_{82}, x_{105}, x_{125}, x_{152} $ $ x_{247}^6 $ $ x_{247}^5, \overline{x_{65}}, $ $ \underline{x_{174}}, x_{204}^{13} $ $ x_{233}^7 $ $ x_{233}^6, \underline{x_{18}}, \overline{x_{47}} $ $ x_{229}^8 $ $ x_{229}^7, \underline{x_{19}}, \overline{x_{60}} $ $ x_{225}^9 $ $ x_{225}^8, x_{21}, x_{79} $
16 $ x_{252}^5 $ $ x_{252}^4, x_{83}, x_{106}, x_{126}, x_{153} $ $ x_{248}^6 $ $ x_{248}^5, \overline{x_{66}}, $ $ \underline{x_{175}}, x_{205}^{13} $ $ x_{234}^7 $ $ x_{234}^6, \underline{x_{19}}, \overline{x_{48}} $ $ x_{230}^8 $ $ x_{230}^7, \underline{x_{20}}, \overline{x_{61}} $ $ x_{226}^9 $ $ x_{226}^8, x_{22}, x_{80} $
17 $ x_{253}^5 $ $ x_{253}^4, x_{84}, x_{107}, x_{127}, x_{154} $ $ x_{249}^6 $ $ x_{249}^5, \overline{x_{67}}, $ $ \underline{x_{176}}, x_{206}^{13} $ $ x_{235}^7 $ $ x_{235}^6, \underline{x_{20}}, \overline{x_{49}} $ $ x_{231}^8 $ $ x_{231}^7, \underline{x_{21}}, \overline{x_{62}} $ $ x_{227}^9 $ $ x_{227}^8, x_{23}, x_{81} $
18 $ x_{254}^5 $ $ x_{254}^4, x_{85}, x_{108}, x_{128}, x_{155} $ $ x_{250}^6 $ $ x_{250}^5, \overline{x_{68}}, $ $ \underline{x_{177}}, x_{207}^{13} $ $ x_{236}^7 $ $ x_{236}^6, \underline{x_{21}}, \overline{x_{50}} $ $ x_{232}^8 $ $ x_{232}^7, \underline{x_{22}}, \overline{x_{63}} $ $ x_{228}^9 $ $ x_{228}^8, x_{24}, x_{82} $
19 $ x_{255}^5 $ $ x_{255}^4, x_{86}, x_{109}, x_{129}, x_{156} $ $ x_{251}^6 $ $ x_{251}^5, \overline{x_{69}}, $ $ \underline{x_{178}}, x_{208}^{13} $ $ x_{237}^7 $ $ x_{237}^6, \underline{x_{22}}, \overline{x_{51}} $ $ x_{233}^8 $ $ x_{233}^7, \underline{x_{23}}, \overline{x_{64}} $ $ x_{229}^9 $ $ x_{229}^8, x_{25}, x_{83} $
20 $ x_{256}^5 $ $ x_{256}^4, x_{87}, x_{110}, x_{130}, x_{157} $ $ x_{252}^6 $ $ x_{252}^5, \overline{x_{70}}, $ $ \underline{x_{179}}, x_{209}^{13} $ $ x_{238}^7 $ $ x_{238}^6, \underline{x_{23}}, \overline{x_{52}} $ $ x_{234}^8 $ $ x_{234}^7, \underline{x_{24}}, \overline{x_{65}} $ $ x_{230}^9 $ $ x_{230}^8, x_{26}, x_{84} $
21 $ x_{257}^5 $ $ x_{257}^4, x_{88}, x_{111}, x_{131}, x_{158} $ $ x_{253}^6 $ $ x_{253}^5, \overline{x_{71}}, $ $ \underline{x_{180}}, x_{210}^{13} $ $ x_{239}^7 $ $ x_{239}^6, \underline{x_{24}}, \overline{x_{53}} $ $ x_{235}^8 $ $ x_{235}^7, \underline{x_{25}}, \overline{x_{66}} $ $ x_{231}^9 $ $ x_{231}^8, x_{27}, x_{85} $
22 $ x_{258}^5 $ $ x_{258}^4, x_{89}, x_{112}, x_{132}, x_{159} $ $ x_{254}^6 $ $ x_{254}^5, \overline{x_{72}}, $ $ \underline{x_{181}}, x_{211}^{13} $ $ x_{240}^7 $ $ x_{240}^6, \underline{x_{25}}, \overline{x_{54}} $ $ x_{236}^8 $ $ x_{236}^7, \underline{x_{26}}, \overline{x_{67}} $ $ x_{232}^9 $ $ x_{232}^8, x_{28}, x_{86} $
23 $ x_{259}^5 $ $ x_{259}^4, x_{90}, x_{113}, x_{133}, x_{160} $ $ x_{255}^6 $ $ x_{255}^5, \overline{x_{73}}, $ $ \underline{x_{182}}, x_{212}^{13} $ $ x_{241}^7 $ $ x_{241}^6, \underline{x_{26}}, \overline{x_{55}} $ $ x_{237}^8 $ $ x_{237}^7, \underline{x_{27}}, \overline{x_{68}} $ $ x_{233}^9 $ $ x_{233}^8, \overline{x_{29}}, \underline{x_{87}} $
24 $ x_{260}^5 $ $ x_{260}^4, x_{91}, x_{114}, x_{134}, x_{161} $ $ x_{256}^6 $ $ x_{256}^5, \overline{x_{74}}, $ $ \underline{x_{183}}, x_{213}^{13} $ $ x_{242}^7 $ $ x_{242}^6, \underline{x_{27}}, \overline{x_{56}} $ $ x_{238}^8 $ $ x_{238}^7, \underline{x_{28}}, \overline{x_{69}} $ $ x_{234}^9 $ $ x_{234}^8, \overline{x_{30}}, \underline{x_{88}} $
25 $ x_{261}^5 $ $ x_{261}^4, x_{92}, x_{115}, x_{135}, x_{162} $ $ x_{257}^6 $ $ x_{257}^5, \overline{x_{75}}, $ $ \underline{x_{184}}, x_{214}^{13} $ $ x_{243}^7 $ $ x_{243}^6, \underline{x_{28}}, \overline{x_{57}} $ $ x_{239}^8 $ $ x_{239}^7, \overline{x_{29}}, \overline{x_{70}} $ $ x_{235}^9 $ $ x_{235}^8, \overline{x_{31}}, \underline{x_{89}} $
26 $ x_{262}^5 $ $ x_{262}^4, x_{93}, x_{116}, x_{136}, x_{163} $ $ x_{258}^6 $ $ x_{258}^5, \overline{x_{76}}, $ $ \underline{x_{185}}, x_{215}^{13} $ $ x_{244}^7 $ $ x_{244}^6, \overline{x_{29}}, \overline{x_{58}} $ $ x_{240}^8 $ $ x_{240}^7, \overline{x_{30}}, \overline{x_{71}} $ $ x_{236}^9 $ $ x_{236}^8, \overline{x_{32}}, \underline{x_{90}} $
27 $ x_{263}^5 $ $ x_{263}^4, x_{94}, x_{117}, x_{137}, x_{164} $ $ x_{259}^6 $ $ x_{259}^5, x_{77}, $ $ x_{186}, x_{216}^{13} $ $ x_{245}^7 $ $ x_{245}^6, \overline{x_{30}}, \overline{x_{59}} $ $ x_{241}^8 $ $ x_{241}^7, \overline{x_{31}}, \overline{x_{72}} $ $ x_{237}^9 $ $ x_{237}^8, \overline{x_{33}}, \underline{x_{91}} $
28 $ x_{264}^5 $ $ x_{264}^4, x_{95}, x_{118}, x_{138}, x_{165} $ $ x_{260}^6 $ $ x_{260}^5, x_{78}, $ $ x_{187}, x_{217}^{13} $ $ x_{246}^7 $ $ x_{246}^6, \overline{x_{31}}, \overline{x_{60}} $ $ x_{242}^8 $ $ x_{242}^7, \overline{x_{32}}, \overline{x_{73}} $ $ x_{238}^9 $ $ x_{238}^8, \overline{x_{34}}, \underline{x_{92}} $
29 $ x_{265}^5 $ $ x_{265}^4, x_{96}, x_{119}, x_{139}, x_{166} $ $ x_{261}^6 $ $ x_{261}^5, x_{79}, $ $ x_{188}, x_{218}^{13} $ $ x_{247}^7 $ $ x_{247}^6, \overline{x_{32}}, \overline{x_{61}} $ $ x_{243}^8 $ $ x_{243}^7, \overline{x_{33}}, \overline{x_{74}} $ $ x_{239}^9 $ $ x_{239}^8, \overline{x_{35}}, \underline{x_{93}} $
30 $ x_{266}^5 $ $ x_{266}^4, x_{97}, x_{120}, x_{140}, x_{167} $ $ x_{262}^6 $ $ x_{262}^5, x_{80}, $ $ x_{189}, x_{219}^{13} $ $ x_{248}^7 $ $ x_{248}^6, \overline{x_{33}}, \overline{x_{62}} $ $ x_{244}^8 $ $ x_{244}^7, \overline{x_{34}}, \overline{x_{75}} $ $ x_{240}^9 $ $ x_{240}^8, \overline{x_{36}}, \underline{x_{94}} $
31 $ x_{267}^5 $ $ x_{267}^4, x_{98}, x_{121}, x_{141}, x_{168} $ $ x_{263}^6 $ $ x_{263}^5, x_{81}, $ $ x_{190}, x_{220}^{13} $ $ x_{249}^7 $ $ x_{249}^6, \overline{x_{34}}, \overline{x_{63}} $ $ x_{245}^8 $ $ x_{245}^7, \overline{x_{35}}, \overline{x_{76}} $ $ x_{241}^9 $ $ x_{241}^8, x_{37}, x_{95} $
32 $ x_{268}^5 $ $ x_{268}^4, x_{99}, x_{122}, x_{142}, x_{169} $ $ x_{264}^6 $ $ x_{264}^5, x_{82}, $ $ x_{191}, x_{221}^{13} $ $ x_{250}^7 $ $ x_{250}^6, \overline{x_{35}}, \overline{x_{64}} $ $ x_{246}^8 $ $ x_{246}^7, \overline{x_{36}},\underline{x_{77}} $ $ x_{242}^9 $ $ x_{242}^8, x_{38}, x_{96} $
33 $ x_{269}^5 $ $ x_{269}^4, x_{100}, x_{123}, x_{143}, x_{170} $ $ x_{265}^6 $ $ x_{265}^5, x_{83}, $ $ x_{192}, x_{222}^{13} $ $ x_{251}^7 $ $ x_{251}^6, \overline{x_{36}}, \overline{x_{65}} $ $ x_{247}^8 $ $ x_{247}^7, x_{37}, x_{78} $ $ x_{243}^9 $ $ x_{243}^8, x_{39}, x_{97} $
34 $ x_{270}^5 $ $ x_{270}^4, x_{101}, x_{124}, x_{144}, x_{171} $ $ x_{266}^6 $ $ x_{266}^5, x_{84}, $ $ x_{193}, x_{223}^{13} $ $ x_{252}^7 $ $ x_{252}^6, \underline{x_{37}}, \overline{x_{66}} $ $ x_{248}^8 $ $ x_{248}^7, x_{38}, x_{79} $ $ x_{244}^9 $ $ x_{244}^8, x_{40}, x_{98} $
Table 3.  State Bits required to calculate feedback bits
Row Feedback bit calculaton because of (15) Column 10 Feedback bit calculaton because of (16) Column11 Feedback bit calculaton because of (17) Column 12 Feedback bit calculaton because of (18) Column 13
Feedback bits State bits appeared on RHS of (15) Feedback bits State bits appeared on RHS of (16) Feedback bits State bits appeared on RHS of (17) Feedback bits State bits appeared on RHS of (18)
0 $ x_{206}^{10} $ $ x_{206}, x_{5}, x_{80} $ $ x_{202}^{11} $ $ x_{202}, x_{8}, $ $ x_{103} $ $ x_{198}^{12} $ $ x_{198}, \overline{x_{29}}, \overline{x_{52}}, \overline{x_{72}}, \underline{x_{99}} $ $ x_{194}^{13} $ $ x_{194}, x_{12}, x_{121} $
1 $ x_{207}^{10} $ $ x_{207}, x_{6}, x_{81} $ $ x_{203}^{11} $ $ x_{203}, x_{9}, $ $ x_{104} $ $ x_{199}^{12} $ $ x_{199}, \overline{x_{30}}, \overline{x_{53}}, \overline{x_{73}}, \underline{x_{100}} $ $ x_{195}^{13} $ $ x_{195}, x_{13}, x_{122} $
2 $ x_{208}^{10} $ $ x_{208}, x_{7}, x_{82} $ $ x_{204}^{11} $ $ x_{204}, x_{10}, $ $ x_{105} $ $ x_{200}^{12} $ $ x_{200}, \overline{x_{31}}, \overline{x_{54}}, \overline{x_{74}}, \underline{x_{101}} $ $ x_{196}^{13} $ $ x_{196}, x_{14}, x_{123} $
3 $ x_{209}^{10} $ $ x_{209}, x_{8}, x_{83} $ $ x_{205}^{11} $ $ x_{205}, x_{11}, $ $ x_{106} $ $ x_{201}^{12} $ $ x_{201}, \overline{x_{32}}, \overline{x_{55}}, \overline{x_{75}}, \underline{x_{102}} $ $ x_{197}^{13} $ $ x_{197}, x_{15}, x_{124} $
4 $ x_{210}^{10} $ $ x_{210}^9, x_{9}, x_{84} $ $ x_{206}^{11} $ $ x_{206}^{10}, x_{12}, $ $ x_{107} $ $ x_{202}^{12} $ $ x_{202}^{11}, \overline{x_{33}}, \overline{x_{56}}, \overline{x_{76}}, \underline{x_{103}} $ $ x_{198}^{13} $ $ x_{198}^{12}, x_{16}, x_{125} $
5 $ x_{211}^{10} $ $ x_{211}^9, x_{10}, x_{85} $ $ x_{207}^{11} $ $ x_{207}^{10}, x_{13}, $ $ x_{108} $ $ x_{203}^{12} $ $ x_{203}^{11}, \overline{x_{34}}, \overline{x_{57}}, \underline{x_{77}}, \underline{x_{104}} $ $ x_{199}^{13} $ $ x_{199}^{12}, x_{17}, x_{126} $
6 $ x_{212}^{10} $ $ x_{212}^9, x_{11}, x_{86} $ $ x_{208}^{11} $ $ x_{208}^{10}, x_{14}, $ $ x_{109} $ $ x_{204}^{12} $ $ x_{204}^{11}, \overline{x_{35}}, \overline{x_{58}}, \underline{x_{78}}, \underline{x_{105}} $ $ x_{200}^{13} $ $ x_{200}^{12}, x_{18}, x_{127} $
7 $ x_{213}^{10} $ $ x_{213}^9, x_{12}, x_{87} $ $ x_{209}^{11} $ $ x_{209}^{10}, x_{15}, $ $ x_{110} $ $ x_{205}^{12} $ $ x_{205}^{11}, \overline{x_{36}}, \overline{x_{59}}, \underline{x_{79}}, \underline{x_{106}} $ $ x_{201}^{13} $ $ x_{201}^{12}, x_{19}, x_{128} $
8 $ x_{214}^{10} $ $ x_{214}^9, x_{13}, x_{88} $ $ x_{210}^{11} $ $ x_{210}^{10}, x_{16}, $ $ x_{111} $ $ x_{206}^{12} $ $ x_{206}^{11}, \underline{x_{37}}, \overline{x_{60}}, \underline{x_{80}}, \underline{x_{107}} $ $ x_{202}^{13} $ $ x_{202}^{12}, x_{20}, x_{129} $
9 $ x_{215}^{10} $ $ x_{215}^9, x_{14}, x_{89} $ $ x_{211}^{11} $ $ x_{211}^{10}, x_{17}, $ $ x_{112} $ $ x_{207}^{12} $ $ x_{207}^{11}, \underline{x_{38}}, \overline{x_{61}}, \underline{x_{81}}, \underline{x_{108}} $ $ x_{203}^{13} $ $ x_{203}^{12}, x_{21}, x_{130} $
10 $ x_{216}^{10} $ $ x_{216}^9, x_{15}, x_{90} $ $ x_{212}^{11} $ $ x_{212}^{10}, x_{18}, $ $ x_{113} $ $ x_{208}^{12} $ $ x_{208}^{11}, \underline{x_{39}}, \overline{x_{62}}, \underline{x_{82}}, \underline{x_{109}} $ $ x_{204}^{13} $ $ x_{204}^{12}, x_{22}, x_{131} $
11 $ x_{217}^{10} $ $ x_{217}^9, x_{16}, x_{91} $ $ x_{213}^{11} $ $ x_{213}^{10}, x_{19}, $ $ x_{114} $ $ x_{209}^{12} $ $ x_{209}^{11}, \underline{x_{40}}, \overline{x_{63}}, \underline{x_{83}}, \underline{x_{110}} $ $ x_{205}^{13} $ $ x_{205}^{12}, x_{23}, x_{132} $
12 $ x_{218}^{10} $ $ x_{218}^9, x_{17}, x_{92} $ $ x_{214}^{11} $ $ x_{214}^{10}, x_{20}, $ $ x_{115} $ $ x_{210}^{12} $ $ x_{210}^{11}, \underline{x_{41}}, \overline{x_{64}}, \underline{x_{84}}, \underline{x_{111}} $ $ x_{206}^{13} $ $ x_{206}^{12}, x_{24}, x_{133} $
13 $ x_{219}^{10} $ $ x_{219}^9, x_{18}, x_{93} $ $ x_{215}^{11} $ $ x_{215}^{10}, x_{21}, $ $ x_{116} $ $ x_{211}^{12} $ $ x_{211}^{11}, \underline{x_{42}}, \overline{x_{65}}, \underline{x_{85}}, \underline{x_{112}} $ $ x_{207}^{13} $ $ x_{207}^{12}, x_{25}, x_{134} $
14 $ x_{220}^{10} $ $ x_{220}^9, x_{19}, x_{94} $ $ x_{216}^{11} $ $ x_{216}^{10}, x_{22}, $ $ x_{117} $ $ x_{212}^{12} $ $ x_{212}^{11}, \underline{x_{43}}, \overline{x_{66}}, \underline{x_{86}}, \underline{x_{113}} $ $ x_{208}^{13} $ $ x_{208}^{12}, x_{26}, x_{135} $
15 $ x_{221}^{10} $ $ x_{221}^9, x_{20}, x_{95} $ $ x_{217}^{11} $ $ x_{217}^{10}, x_{23}, $ $ x_{118} $ $ x_{213}^{12} $ $ x_{213}^{11}, \underline{x_{44}}, \overline{x_{67}}, \underline{x_{87}}, \underline{x_{114}} $ $ x_{209}^{13} $ $ x_{209}^{12}, x_{27}, x_{136} $
16 $ x_{222}^{10} $ $ x_{222}^9, x_{21}, x_{96} $ $ x_{218}^{11} $ $ x_{218}^{10}, x_{24}, $ $ x_{119} $ $ x_{214}^{12} $ $ x_{214}^{11}, \underline{x_{45}}, \overline{x_{68}}, \underline{x_{88}}, \underline{x_{115}} $ $ x_{210}^{13} $ $ x_{210}^{12}, x_{28}, x_{137} $
17 $ x_{223}^{10} $ $ x_{223}^9, x_{22}, x_{97} $ $ x_{219}^{11} $ $ x_{219}^{10}, x_{25}, $ $ x_{120} $ $ x_{215}^{12} $ $ x_{215}^{11}, \overline{x_{46}}, \overline{x_{69}}, \underline{x_{89}}, \underline{x_{116}} $ $ x_{211}^{13} $ $ x_{211}^{12}, \overline{x_{29}}, \underline{x_{138}} $
18 $ x_{224}^{10} $ $ x_{224}^9, x_{23}, x_{98} $ $ x_{220}^{11} $ $ x_{220}^{10}, x_{26}, $ $ x_{121} $ $ x_{216}^{12} $ $ x_{216}^{11}, \overline{x_{47}}, \overline{x_{70}}, \underline{x_{90}}, \underline{x_{117}} $ $ x_{212}^{13} $ $ x_{212}^{12}, \overline{x_{30}}, \underline{x_{139}} $
19 $ x_{225}^{10} $ $ x_{225}^9, x_{24}, x_{99} $ $ x_{221}^{11} $ $ x_{221}^{10}, x_{27}, $ $ x_{122} $ $ x_{217}^{12} $ $ x_{217}^{11}, \overline{x_{48}}, \overline{x_{71}}, \underline{x_{91}}, \underline{x_{118}} $ $ x_{213}^{13} $ $ x_{213}^{12}, \overline{x_{31}}, \underline{x_{140}} $
20 $ x_{226}^{10} $ $ x_{226}^9, x_{25}, x_{100} $ $ x_{222}^{11} $ $ x_{222}^{10}, x_{28}, $ $ x_{123} $ $ x_{218}^{12} $ $ x_{218}^{11}, \overline{x_{49}}, \overline{x_{72}}, \underline{x_{92}}, \underline{x_{119}} $ $ x_{214}^{13} $ $ x_{214}^{12}, \overline{x_{32}}, \underline{x_{141}} $
21 $ x_{227}^{10} $ $ x_{227}^9, x_{26}, x_{101} $ $ x_{223}^{11} $ $ x_{223}^{10}, \overline{x_{29}}, $ $ \underline{x_{124}} $ $ x_{219}^{12} $ $ x_{219}^{11}, \overline{x_{50}}, \overline{x_{73}}, \underline{x_{93}}, \underline{x_{120}} $ $ x_{215}^{13} $ $ x_{215}^{12}, \overline{x_{33}}, \underline{x_{142}} $
22 $ x_{228}^{10} $ $ x_{228}^9, x_{27}, x_{102} $ $ x_{224}^{11} $ $ x_{224}^{10}, \overline{x_{30}}, $ $ \underline{x_{125}} $ $ x_{220}^{12} $ $ x_{220}^{11}, \overline{x_{51}}, \overline{x_{74}}, \underline{x_{94}}, \underline{x_{121}} $ $ x_{216}^{13} $ $ x_{216}^{12}, \overline{x_{34}}, \underline{x_{143}} $
23 $ x_{229}^{10} $ $ x_{229}^9, x_{28}, x_{103} $ $ x_{225}^{11} $ $ x_{225}^{10}, \overline{x_{31}}, $ $ \underline{x_{126}} $ $ x_{221}^{12} $ $ x_{221}^{11}, \overline{x_{52}}, \overline{x_{75}}, \underline{x_{95}}, \underline{x_{122}} $ $ x_{217}^{13} $ $ x_{217}^{12}, \overline{x_{35}}, \underline{x_{144}} $
24 $ x_{230}^{10} $ $ x_{230}^9, \overline{x_{29}}, \underline{x_{104}} $ $ x_{226}^{11} $ $ x_{226}^{10}, \overline{x_{32}}, $ $ \underline{x_{127}} $ $ x_{222}^{12} $ $ x_{222}^{11}, \overline{x_{53}}, \overline{x_{76}}, \underline{x_{96}}, \underline{x_{123}} $ $ x_{218}^{13} $ $ x_{218}^{12}, \overline{x_{36}}, \underline{x_{145}} $
25 $ x_{231}^{10} $ $ x_{231}^9, \overline{x_{30}}, \underline{x_{105}} $ $ x_{227}^{11} $ $ x_{227}^{10}, \overline{x_{33}}, $ $ \underline{x_{128}} $ $ x_{223}^{12} $ $ x_{223}^{11}, \overline{x_{54}}, \underline{x_{77}}, \underline{x_{97}}, \underline{x_{124}} $ $ x_{219}^{13} $ $ x_{219}^{12}, x_{37}, x_{146} $
26 $ x_{232}^{10} $ $ x_{232}^9, \overline{x_{31}}, \underline{x_{106}} $ $ x_{228}^{11} $ $ x_{228}^{10}, \overline{x_{34}}, $ $ \underline{x_{129}} $ $ x_{224}^{12} $ $ x_{224}^{11}, \overline{x_{55}}, \underline{x_{78}}, \underline{x_{98}}, \underline{x_{125}} $ $ x_{220}^{13} $ $ x_{220}^{12}, x_{38}, x_{147} $
27 $ x_{233}^{10} $ $ x_{233}^9, \overline{x_{32}}, \underline{x_{107}} $ $ x_{229}^{11} $ $ x_{229}^{10}, \overline{x_{35}}, $ $ \underline{x_{130}} $ $ x_{225}^{12} $ $ x_{225}^{11}, \overline{x_{56}}, \underline{x_{79}}, \underline{x_{99}}, \underline{x_{126}} $ $ x_{221}^{13} $ $ x_{221}^{12}, x_{39}, x_{148} $
28 $ x_{234}^{10} $ $ x_{234}^9, \overline{x_{33}}, \underline{x_{108}} $ $ x_{230}^{11} $ $ x_{230}^{10}, \overline{x_{36}}, $ $ \underline{x_{131}} $ $ x_{226}^{12} $ $ x_{226}^{11}, \overline{x_{57}}, \underline{x_{80}}, \underline{x_{100}}, \underline{x_{127}} $ $ x_{222}^{13} $ $ x_{222}^{12}, x_{40}, x_{149} $
29 $ x_{235}^{10} $ $ x_{235}^9, \overline{x_{34}}, \underline{x_{109}} $ $ x_{231}^{11} $ $ x_{231}^{10}, x_{37}, $ $ x_{132} $ $ x_{227}^{12} $ $ x_{227}^{11}, \overline{x_{58}}, \underline{x_{81}}, \underline{x_{101}}, \underline{x_{128}} $ $ x_{223}^{13} $ $ x_{223}^{12}, x_{41}, x_{150} $
30 $ x_{236}^{10} $ $ x_{236}^9, \overline{x_{35}}, \underline{x_{110}} $ $ x_{232}^{11} $ $ x_{232}^{10}, x_{38}, $ $ x_{133} $ $ x_{228}^{12} $ $ x_{228}^{11}, \overline{x_{59}}, \underline{x_{82}}, \underline{x_{102}}, \underline{x_{129}} $ $ x_{224}^{13} $ $ x_{224}^{12}, x_{42}, x_{151} $
31 $ x_{237}^{10} $ $ x_{237}^9, \overline{x_{36}}, \underline{x_{111}} $ $ x_{233}^{11} $ $ x_{233}^{10}, x_{39}, $ $ x_{134} $ $ x_{229}^{12} $ $ x_{229}^{11}, \overline{x_{60}}, \underline{x_{83}}, \underline{x_{103}}, \underline{x_{130}} $ $ x_{225}^{13} $ $ x_{225}^{12}, x_{43}, x_{152} $
32 $ x_{238}^{10} $ $ x_{238}^9, x_{37}, x_{112} $ $ x_{234}^{11} $ $ x_{234}^{10}, x_{40}, $ $ x_{135} $ $ x_{230}^{12} $ $ x_{230}^{11}, \overline{x_{61}}, \underline{x_{84}}, \underline{x_{104}}, \underline{x_{131}} $ $ x_{226}^{13} $ $ x_{226}^{12}, x_{44}, x_{153} $
33 $ x_{239}^{10} $ $ x_{239}^9, x_{38}, x_{113} $ $ x_{235}^{11} $ $ x_{235}^{10}, x_{41}, $ $ x_{136} $ $ x_{231}^{12} $ $ x_{231}^{11}, \overline{x_{62}}, \underline{x_{85}}, \underline{x_{105}}, \underline{x_{132}} $ $ x_{227}^{13} $ $ x_{227}^{12}, x_{45}, x_{154} $
34 $ x_{240}^{10} $ $ x_{240}^9, x_{39}, x_{114} $ $ x_{236}^{11} $ $ x_{236}^{10}, x_{42}, $ $ x_{137} $ $ x_{232}^{12} $ $ x_{232}^{11}, \overline{x_{63}}, \underline{x_{86}}, \underline{x_{106}}, \underline{x_{133}} $ $ x_{228}^{13} $ $ x_{228}^{12}, \overline{x_{46}}, \underline{x_{155}} $
Row Feedback bit calculaton because of (15) Column 10 Feedback bit calculaton because of (16) Column11 Feedback bit calculaton because of (17) Column 12 Feedback bit calculaton because of (18) Column 13
Feedback bits State bits appeared on RHS of (15) Feedback bits State bits appeared on RHS of (16) Feedback bits State bits appeared on RHS of (17) Feedback bits State bits appeared on RHS of (18)
0 $ x_{206}^{10} $ $ x_{206}, x_{5}, x_{80} $ $ x_{202}^{11} $ $ x_{202}, x_{8}, $ $ x_{103} $ $ x_{198}^{12} $ $ x_{198}, \overline{x_{29}}, \overline{x_{52}}, \overline{x_{72}}, \underline{x_{99}} $ $ x_{194}^{13} $ $ x_{194}, x_{12}, x_{121} $
1 $ x_{207}^{10} $ $ x_{207}, x_{6}, x_{81} $ $ x_{203}^{11} $ $ x_{203}, x_{9}, $ $ x_{104} $ $ x_{199}^{12} $ $ x_{199}, \overline{x_{30}}, \overline{x_{53}}, \overline{x_{73}}, \underline{x_{100}} $ $ x_{195}^{13} $ $ x_{195}, x_{13}, x_{122} $
2 $ x_{208}^{10} $ $ x_{208}, x_{7}, x_{82} $ $ x_{204}^{11} $ $ x_{204}, x_{10}, $ $ x_{105} $ $ x_{200}^{12} $ $ x_{200}, \overline{x_{31}}, \overline{x_{54}}, \overline{x_{74}}, \underline{x_{101}} $ $ x_{196}^{13} $ $ x_{196}, x_{14}, x_{123} $
3 $ x_{209}^{10} $ $ x_{209}, x_{8}, x_{83} $ $ x_{205}^{11} $ $ x_{205}, x_{11}, $ $ x_{106} $ $ x_{201}^{12} $ $ x_{201}, \overline{x_{32}}, \overline{x_{55}}, \overline{x_{75}}, \underline{x_{102}} $ $ x_{197}^{13} $ $ x_{197}, x_{15}, x_{124} $
4 $ x_{210}^{10} $ $ x_{210}^9, x_{9}, x_{84} $ $ x_{206}^{11} $ $ x_{206}^{10}, x_{12}, $ $ x_{107} $ $ x_{202}^{12} $ $ x_{202}^{11}, \overline{x_{33}}, \overline{x_{56}}, \overline{x_{76}}, \underline{x_{103}} $ $ x_{198}^{13} $ $ x_{198}^{12}, x_{16}, x_{125} $
5 $ x_{211}^{10} $ $ x_{211}^9, x_{10}, x_{85} $ $ x_{207}^{11} $ $ x_{207}^{10}, x_{13}, $ $ x_{108} $ $ x_{203}^{12} $ $ x_{203}^{11}, \overline{x_{34}}, \overline{x_{57}}, \underline{x_{77}}, \underline{x_{104}} $ $ x_{199}^{13} $ $ x_{199}^{12}, x_{17}, x_{126} $
6 $ x_{212}^{10} $ $ x_{212}^9, x_{11}, x_{86} $ $ x_{208}^{11} $ $ x_{208}^{10}, x_{14}, $ $ x_{109} $ $ x_{204}^{12} $ $ x_{204}^{11}, \overline{x_{35}}, \overline{x_{58}}, \underline{x_{78}}, \underline{x_{105}} $ $ x_{200}^{13} $ $ x_{200}^{12}, x_{18}, x_{127} $
7 $ x_{213}^{10} $ $ x_{213}^9, x_{12}, x_{87} $ $ x_{209}^{11} $ $ x_{209}^{10}, x_{15}, $ $ x_{110} $ $ x_{205}^{12} $ $ x_{205}^{11}, \overline{x_{36}}, \overline{x_{59}}, \underline{x_{79}}, \underline{x_{106}} $ $ x_{201}^{13} $ $ x_{201}^{12}, x_{19}, x_{128} $
8 $ x_{214}^{10} $ $ x_{214}^9, x_{13}, x_{88} $ $ x_{210}^{11} $ $ x_{210}^{10}, x_{16}, $ $ x_{111} $ $ x_{206}^{12} $ $ x_{206}^{11}, \underline{x_{37}}, \overline{x_{60}}, \underline{x_{80}}, \underline{x_{107}} $ $ x_{202}^{13} $ $ x_{202}^{12}, x_{20}, x_{129} $
9 $ x_{215}^{10} $ $ x_{215}^9, x_{14}, x_{89} $ $ x_{211}^{11} $ $ x_{211}^{10}, x_{17}, $ $ x_{112} $ $ x_{207}^{12} $ $ x_{207}^{11}, \underline{x_{38}}, \overline{x_{61}}, \underline{x_{81}}, \underline{x_{108}} $ $ x_{203}^{13} $ $ x_{203}^{12}, x_{21}, x_{130} $
10 $ x_{216}^{10} $ $ x_{216}^9, x_{15}, x_{90} $ $ x_{212}^{11} $ $ x_{212}^{10}, x_{18}, $ $ x_{113} $ $ x_{208}^{12} $ $ x_{208}^{11}, \underline{x_{39}}, \overline{x_{62}}, \underline{x_{82}}, \underline{x_{109}} $ $ x_{204}^{13} $ $ x_{204}^{12}, x_{22}, x_{131} $
11 $ x_{217}^{10} $ $ x_{217}^9, x_{16}, x_{91} $ $ x_{213}^{11} $ $ x_{213}^{10}, x_{19}, $ $ x_{114} $ $ x_{209}^{12} $ $ x_{209}^{11}, \underline{x_{40}}, \overline{x_{63}}, \underline{x_{83}}, \underline{x_{110}} $ $ x_{205}^{13} $ $ x_{205}^{12}, x_{23}, x_{132} $
12 $ x_{218}^{10} $ $ x_{218}^9, x_{17}, x_{92} $ $ x_{214}^{11} $ $ x_{214}^{10}, x_{20}, $ $ x_{115} $ $ x_{210}^{12} $ $ x_{210}^{11}, \underline{x_{41}}, \overline{x_{64}}, \underline{x_{84}}, \underline{x_{111}} $ $ x_{206}^{13} $ $ x_{206}^{12}, x_{24}, x_{133} $
13 $ x_{219}^{10} $ $ x_{219}^9, x_{18}, x_{93} $ $ x_{215}^{11} $ $ x_{215}^{10}, x_{21}, $ $ x_{116} $ $ x_{211}^{12} $ $ x_{211}^{11}, \underline{x_{42}}, \overline{x_{65}}, \underline{x_{85}}, \underline{x_{112}} $ $ x_{207}^{13} $ $ x_{207}^{12}, x_{25}, x_{134} $
14 $ x_{220}^{10} $ $ x_{220}^9, x_{19}, x_{94} $ $ x_{216}^{11} $ $ x_{216}^{10}, x_{22}, $ $ x_{117} $ $ x_{212}^{12} $ $ x_{212}^{11}, \underline{x_{43}}, \overline{x_{66}}, \underline{x_{86}}, \underline{x_{113}} $ $ x_{208}^{13} $ $ x_{208}^{12}, x_{26}, x_{135} $
15 $ x_{221}^{10} $ $ x_{221}^9, x_{20}, x_{95} $ $ x_{217}^{11} $ $ x_{217}^{10}, x_{23}, $ $ x_{118} $ $ x_{213}^{12} $ $ x_{213}^{11}, \underline{x_{44}}, \overline{x_{67}}, \underline{x_{87}}, \underline{x_{114}} $ $ x_{209}^{13} $ $ x_{209}^{12}, x_{27}, x_{136} $
16 $ x_{222}^{10} $ $ x_{222}^9, x_{21}, x_{96} $ $ x_{218}^{11} $ $ x_{218}^{10}, x_{24}, $ $ x_{119} $ $ x_{214}^{12} $ $ x_{214}^{11}, \underline{x_{45}}, \overline{x_{68}}, \underline{x_{88}}, \underline{x_{115}} $ $ x_{210}^{13} $ $ x_{210}^{12}, x_{28}, x_{137} $
17 $ x_{223}^{10} $ $ x_{223}^9, x_{22}, x_{97} $ $ x_{219}^{11} $ $ x_{219}^{10}, x_{25}, $ $ x_{120} $ $ x_{215}^{12} $ $ x_{215}^{11}, \overline{x_{46}}, \overline{x_{69}}, \underline{x_{89}}, \underline{x_{116}} $ $ x_{211}^{13} $ $ x_{211}^{12}, \overline{x_{29}}, \underline{x_{138}} $
18 $ x_{224}^{10} $ $ x_{224}^9, x_{23}, x_{98} $ $ x_{220}^{11} $ $ x_{220}^{10}, x_{26}, $ $ x_{121} $ $ x_{216}^{12} $ $ x_{216}^{11}, \overline{x_{47}}, \overline{x_{70}}, \underline{x_{90}}, \underline{x_{117}} $ $ x_{212}^{13} $ $ x_{212}^{12}, \overline{x_{30}}, \underline{x_{139}} $
19 $ x_{225}^{10} $ $ x_{225}^9, x_{24}, x_{99} $ $ x_{221}^{11} $ $ x_{221}^{10}, x_{27}, $ $ x_{122} $ $ x_{217}^{12} $ $ x_{217}^{11}, \overline{x_{48}}, \overline{x_{71}}, \underline{x_{91}}, \underline{x_{118}} $ $ x_{213}^{13} $ $ x_{213}^{12}, \overline{x_{31}}, \underline{x_{140}} $
20 $ x_{226}^{10} $ $ x_{226}^9, x_{25}, x_{100} $ $ x_{222}^{11} $ $ x_{222}^{10}, x_{28}, $ $ x_{123} $ $ x_{218}^{12} $ $ x_{218}^{11}, \overline{x_{49}}, \overline{x_{72}}, \underline{x_{92}}, \underline{x_{119}} $ $ x_{214}^{13} $ $ x_{214}^{12}, \overline{x_{32}}, \underline{x_{141}} $
21 $ x_{227}^{10} $ $ x_{227}^9, x_{26}, x_{101} $ $ x_{223}^{11} $ $ x_{223}^{10}, \overline{x_{29}}, $ $ \underline{x_{124}} $ $ x_{219}^{12} $ $ x_{219}^{11}, \overline{x_{50}}, \overline{x_{73}}, \underline{x_{93}}, \underline{x_{120}} $ $ x_{215}^{13} $ $ x_{215}^{12}, \overline{x_{33}}, \underline{x_{142}} $
22 $ x_{228}^{10} $ $ x_{228}^9, x_{27}, x_{102} $ $ x_{224}^{11} $ $ x_{224}^{10}, \overline{x_{30}}, $ $ \underline{x_{125}} $ $ x_{220}^{12} $ $ x_{220}^{11}, \overline{x_{51}}, \overline{x_{74}}, \underline{x_{94}}, \underline{x_{121}} $ $ x_{216}^{13} $ $ x_{216}^{12}, \overline{x_{34}}, \underline{x_{143}} $
23 $ x_{229}^{10} $ $ x_{229}^9, x_{28}, x_{103} $ $ x_{225}^{11} $ $ x_{225}^{10}, \overline{x_{31}}, $ $ \underline{x_{126}} $ $ x_{221}^{12} $ $ x_{221}^{11}, \overline{x_{52}}, \overline{x_{75}}, \underline{x_{95}}, \underline{x_{122}} $ $ x_{217}^{13} $ $ x_{217}^{12}, \overline{x_{35}}, \underline{x_{144}} $
24 $ x_{230}^{10} $ $ x_{230}^9, \overline{x_{29}}, \underline{x_{104}} $ $ x_{226}^{11} $ $ x_{226}^{10}, \overline{x_{32}}, $ $ \underline{x_{127}} $ $ x_{222}^{12} $ $ x_{222}^{11}, \overline{x_{53}}, \overline{x_{76}}, \underline{x_{96}}, \underline{x_{123}} $ $ x_{218}^{13} $ $ x_{218}^{12}, \overline{x_{36}}, \underline{x_{145}} $
25 $ x_{231}^{10} $ $ x_{231}^9, \overline{x_{30}}, \underline{x_{105}} $ $ x_{227}^{11} $ $ x_{227}^{10}, \overline{x_{33}}, $ $ \underline{x_{128}} $ $ x_{223}^{12} $ $ x_{223}^{11}, \overline{x_{54}}, \underline{x_{77}}, \underline{x_{97}}, \underline{x_{124}} $ $ x_{219}^{13} $ $ x_{219}^{12}, x_{37}, x_{146} $
26 $ x_{232}^{10} $ $ x_{232}^9, \overline{x_{31}}, \underline{x_{106}} $ $ x_{228}^{11} $ $ x_{228}^{10}, \overline{x_{34}}, $ $ \underline{x_{129}} $ $ x_{224}^{12} $ $ x_{224}^{11}, \overline{x_{55}}, \underline{x_{78}}, \underline{x_{98}}, \underline{x_{125}} $ $ x_{220}^{13} $ $ x_{220}^{12}, x_{38}, x_{147} $
27 $ x_{233}^{10} $ $ x_{233}^9, \overline{x_{32}}, \underline{x_{107}} $ $ x_{229}^{11} $ $ x_{229}^{10}, \overline{x_{35}}, $ $ \underline{x_{130}} $ $ x_{225}^{12} $ $ x_{225}^{11}, \overline{x_{56}}, \underline{x_{79}}, \underline{x_{99}}, \underline{x_{126}} $ $ x_{221}^{13} $ $ x_{221}^{12}, x_{39}, x_{148} $
28 $ x_{234}^{10} $ $ x_{234}^9, \overline{x_{33}}, \underline{x_{108}} $ $ x_{230}^{11} $ $ x_{230}^{10}, \overline{x_{36}}, $ $ \underline{x_{131}} $ $ x_{226}^{12} $ $ x_{226}^{11}, \overline{x_{57}}, \underline{x_{80}}, \underline{x_{100}}, \underline{x_{127}} $ $ x_{222}^{13} $ $ x_{222}^{12}, x_{40}, x_{149} $
29 $ x_{235}^{10} $ $ x_{235}^9, \overline{x_{34}}, \underline{x_{109}} $ $ x_{231}^{11} $ $ x_{231}^{10}, x_{37}, $ $ x_{132} $ $ x_{227}^{12} $ $ x_{227}^{11}, \overline{x_{58}}, \underline{x_{81}}, \underline{x_{101}}, \underline{x_{128}} $ $ x_{223}^{13} $ $ x_{223}^{12}, x_{41}, x_{150} $
30 $ x_{236}^{10} $ $ x_{236}^9, \overline{x_{35}}, \underline{x_{110}} $ $ x_{232}^{11} $ $ x_{232}^{10}, x_{38}, $ $ x_{133} $ $ x_{228}^{12} $ $ x_{228}^{11}, \overline{x_{59}}, \underline{x_{82}}, \underline{x_{102}}, \underline{x_{129}} $ $ x_{224}^{13} $ $ x_{224}^{12}, x_{42}, x_{151} $
31 $ x_{237}^{10} $ $ x_{237}^9, \overline{x_{36}}, \underline{x_{111}} $ $ x_{233}^{11} $ $ x_{233}^{10}, x_{39}, $ $ x_{134} $ $ x_{229}^{12} $ $ x_{229}^{11}, \overline{x_{60}}, \underline{x_{83}}, \underline{x_{103}}, \underline{x_{130}} $ $ x_{225}^{13} $ $ x_{225}^{12}, x_{43}, x_{152} $
32 $ x_{238}^{10} $ $ x_{238}^9, x_{37}, x_{112} $ $ x_{234}^{11} $ $ x_{234}^{10}, x_{40}, $ $ x_{135} $ $ x_{230}^{12} $ $ x_{230}^{11}, \overline{x_{61}}, \underline{x_{84}}, \underline{x_{104}}, \underline{x_{131}} $ $ x_{226}^{13} $ $ x_{226}^{12}, x_{44}, x_{153} $
33 $ x_{239}^{10} $ $ x_{239}^9, x_{38}, x_{113} $ $ x_{235}^{11} $ $ x_{235}^{10}, x_{41}, $ $ x_{136} $ $ x_{231}^{12} $ $ x_{231}^{11}, \overline{x_{62}}, \underline{x_{85}}, \underline{x_{105}}, \underline{x_{132}} $ $ x_{227}^{13} $ $ x_{227}^{12}, x_{45}, x_{154} $
34 $ x_{240}^{10} $ $ x_{240}^9, x_{39}, x_{114} $ $ x_{236}^{11} $ $ x_{236}^{10}, x_{42}, $ $ x_{137} $ $ x_{232}^{12} $ $ x_{232}^{11}, \overline{x_{63}}, \underline{x_{86}}, \underline{x_{106}}, \underline{x_{133}} $ $ x_{228}^{13} $ $ x_{228}^{12}, \overline{x_{46}}, \underline{x_{155}} $
Table 4.  Equations used for recovery of 35 bits of the internal state
Step/Row Equations used for recovery
0 $\begin{aligned}x_{137}& = z_ 0 \oplus x_{ 80} \oplus x_{99} \oplus x_{227} \oplus x_{222} \oplus x_{187} \oplus x_{243}x_{217} \oplus x_{247}x_{231} \oplus x_{213}x_{235} \\ & \quad \oplus x_{255}x_{251} \oplus x_{181}x_{239} \oplus x_{174}x_{44}\oplus x_{164} \overline{x_{29}} \oplus x_{255}x_{247}x_{243}x_{213}x_{181}x_{174}\end{aligned}$
1 $\begin{aligned}x_{ 138}& = z_ 1 \oplus x_{ 81} \oplus x_{ 100} \oplus x_{ 228} \oplus x_{ 223} \oplus x_{188} \oplus x_{ 244}^3x_{218}^7 \oplus x_{ 248}^2x_{ 232}^6 \oplus x_{214}^8x_{236}^5 \\ & \quad\oplus x_{ 256}^0x_{252}^1 \oplus x_{182}x_{240}^4 \oplus x_{175}x_{ 45}\oplus x_{165} \overline{x_{30}} \oplus x_{256}^0x_{248}^2x_{244}^3x_{214}^8x_{182}x_{175}\end{aligned}$
2 $\begin{aligned}x_{ 139}& = z_ 2 \oplus x_{ 82} \oplus x_{ 101} \oplus x_{ 229} \oplus x_{ 224} \oplus x_{189} \oplus x_{ 245}^3x_{219}^7 \oplus x_{ 249}^2x_{ 233}^6 \oplus x_{215}^8x_{237}^5\\ & \quad\oplus x_{ 257}^0x_{253}^1 \oplus x_{183}x_{241}^4 \oplus x_{176}\overline{x_{ 46}}\oplus x_{166} \overline{x_{31}} \oplus x_{257}^0x_{249}^2x_{245}^3x_{215}^8x_{183}x_{176}\end{aligned}$
3 $\begin{aligned}x_{ 140}& = z_ 3 \oplus x_{ 83} \oplus x_{ 102} \oplus x_{ 230} \oplus x_{ 225} \oplus x_{190} \oplus x_{ 246}^3x_{220}^7 \oplus x_{ 250}^2x_{ 234}^6 \oplus x_{216}^8x_{238}^5\\ & \quad\oplus x_{ 258}^0x_{254}^1 \oplus x_{184}x_{242}^4 \oplus x_{177}\overline{x_{ 47}}\oplus x_{167} \overline{x_{32}} \oplus x_{258}^0x_{250}^2x_{246}^3x_{216}^8x_{184}x_{177}\end{aligned}$
4 $\begin{aligned}x_{ 141}& = z_ 4 \oplus x_{ 84} \oplus x_{ 103} \oplus x_{ 231} \oplus x_{ 226} \oplus x_{191} \oplus x_{ 247}^3x_{221}^7 \oplus x_{ 251}^2x_{ 235}^6 \oplus x_{217}^8x_{239}^5\\ & \quad\oplus x_{ 259}^0x_{255}^1 \oplus x_{185}x_{243}^4 \oplus x_{178}\overline{x_{ 48}}\oplus x_{168} \overline{x_{33}} \oplus x_{259}^0x_{251}^2x_{247}^3x_{217}^8x_{185}x_{178}\end{aligned}$
5 $\begin{aligned}x_{ 142}& = z_ 5 \oplus x_{ 85} \oplus x_{ 104} \oplus x_{ 232}^6 \oplus x_{ 227} \oplus x_{192} \oplus x_{ 248}^3x_{222}^7 \oplus x_{ 252}^2x_{ 236}^6 \oplus x_{218}^8x_{240}^5\\ & \quad \oplus x_{ 260}^0x_{256}^1 \oplus x_{186}x_{244}^4 \oplus x_{179}\overline{x_{ 49}}\oplus x_{169}\overline{x_{34}} \oplus x_{260}^0x_{252}^2x_{248}^3x_{218}^8x_{186}x_{179}\end{aligned}$
6 $\begin{aligned}x_{ 143}& = z_ 6 \oplus x_{ 86} \oplus x_{ 105} \oplus x_{ 233}^6 \oplus x_{ 228} \oplus x_{193} \oplus x_{ 249}^3x_{223}^7 \oplus x_{ 253}^2x_{ 237}^6 \oplus x_{219}^8x_{241}^5\\ & \quad \oplus x_{ 261}^0x_{257}^1 \oplus x_{187}x_{245}^4 \oplus x_{180}\overline{x_{ 50}}\oplus x_{170}\overline{x_{35}} \oplus x_{261}^0x_{253}^2x_{249}^3x_{219}^8x_{187}x_{180}\end{aligned}$
7 $\begin{aligned}x_{ 144}& = z_ 7 \oplus x_{ 87} \oplus x_{ 106} \oplus x_{ 234}^6 \oplus x_{ 229} \oplus x_{194}^{13} \oplus x_{ 250}^3x_{224}^7 \oplus x_{ 254}^2x_{ 238}^6 \oplus x_{220}^8x_{242}^5\\ & \quad \oplus x_{ 262}^0x_{258}^1 \oplus x_{188}x_{246}^4 \oplus x_{181}\overline{x_{ 51}}\oplus x_{171}\overline{x_{36}} \oplus x_{262}^0x_{254}^2x_{250}^3x_{220}^8x_{188}x_{181}\end{aligned}$
8 $\begin{aligned}x_{ 145}& = z_ 8 \oplus x_{ 88} \oplus x_{ 107} \oplus x_{ 235}^6 \oplus x_{ 230} \oplus x_{195}^{13} \oplus x_{ 251}^3x_{225}^7 \oplus x_{ 255}^2x_{ 239}^6 \oplus x_{221}^8x_{243}^5\\ & \quad\oplus x_{ 263}^0x_{259}^1 \oplus x_{189}x_{247}^4 \oplus x_{182}\overline{x_{ 52}}\oplus x_{172}x_{37} \oplus x_{263}^0x_{255}^2x_{251}^3x_{221}^8x_{189}x_{182}\end{aligned}$
9 $\begin{aligned}x_{ 146}& = z_ 9 \oplus x_{ 89} \oplus x_{ 108} \oplus x_{ 236}^6 \oplus x_{ 231} \oplus x_{196}^{13} \oplus x_{ 252}^3x_{226}^7 \oplus x_{ 256}^2x_{ 240}^6 \oplus x_{222}^8x_{244}^5\\ & \quad \oplus x_{ 264}^0x_{260}^1 \oplus x_{190}x_{248}^4 \oplus x_{183}\overline{x_{ 53}}\oplus x_{173}x_{38} \oplus x_{264}^0x_{256}^2x_{252}^3x_{222}^8x_{190}x_{183}\end{aligned}$
10 $\begin{aligned}x_{ 147}& = z_ {10} \oplus x_{ 90} \oplus x_{ 109} \oplus x_{ 237}^6 \oplus x_{ 232}^6 \oplus x_{197}^{13} \oplus x_{ 253}^3x_{227}^7 \oplus x_{ 257}^2x_{ 241}^6 \oplus x_{223}^8x_{245}^5\\ & \quad\oplus x_{ 265}^0x_{261}^1 \oplus x_{191}x_{249}^4 \oplus x_{184}\overline{x_{ 54}}\oplus x_{174}x_{39} \oplus x_{265}^0x_{257}^2x_{253}^3x_{223}^8x_{191}x_{184}\end{aligned}$
11 $\begin{aligned}x_{ 148}& = z_ {11} \oplus x_{ 91} \oplus x_{ 110} \oplus x_{ 238}^6 \oplus x_{ 233}^6 \oplus x_{198}^{13} \oplus x_{ 254}^3x_{228}^7 \oplus x_{ 258}^2x_{ 242}^6 \oplus x_{224}^8x_{246}^5\\ & \quad \oplus x_{ 266}^0x_{262}^1 \oplus x_{192}x_{250}^4 \oplus x_{185}\overline{x_{ 55}}\oplus x_{175}x_{40} \oplus x_{266}^0x_{258}^2x_{254}^3x_{224}^8x_{192}x_{185}\end{aligned}$
12 $\begin{aligned}x_{ 149}& = z_ {12} \oplus x_{ 92} \oplus x_{ 111} \oplus x_{ 239}^6 \oplus x_{ 234}^6 \oplus x_{199}^{13} \oplus x_{ 255}^3x_{229}^7 \oplus x_{ 259}^2x_{ 243}^6 \oplus x_{225}^8x_{247}^5\\ & \quad\oplus x_{ 267}^0x_{263}^1 \oplus x_{193}x_{251}^4 \oplus x_{186}\overline{x_{ 56}}\oplus x_{176}x_{41} \oplus x_{267}^0x_{259}^2x_{255}^3x_{225}^8x_{193}x_{186}\end{aligned}$
13 $\begin{aligned}x_{ 150}& = z_ {13} \oplus x_{ 93} \oplus x_{ 112} \oplus x_{ 240}^6 \oplus x_{ 235}^6 \oplus x_{200}^{13} \oplus x_{ 256}^3x_{230}^7 \oplus x_{ 260}^2x_{ 244}^6 \oplus x_{226}^8x_{248}^5\\ & \quad\oplus x_{ 268}^0x_{264}^1 \oplus x_{194}^{13}x_{252}^4 \oplus x_{187}\overline{x_{ 57}}\oplus x_{177}x_{42} \oplus x_{268}^0x_{260}^2x_{256}^3x_{226}^8x_{194}^{13}x_{187}\end{aligned}$
14 $\begin{aligned}x_{ 151}& = z_ {14} \oplus x_{ 94} \oplus x_{ 113} \oplus x_{ 241}^6 \oplus x_{ 236}^6 \oplus x_{201}^{13} \oplus x_{ 257}^3x_{231}^7 \oplus x_{ 261}^2x_{ 245}^6 \oplus x_{227}^8x_{249}^5\\ & \quad\oplus x_{ 269}^0x_{265}^1 \oplus x_{195}^{13}x_{253}^4 \oplus x_{188}\overline{x_{ 58}}\oplus x_{178}x_{43} \oplus x_{269}^0x_{261}^2x_{257}^3x_{227}^8x_{195}^{13}x_{188}\end{aligned}$
15 $\begin{aligned}x_{ 152}& = z_ {15} \oplus x_{ 95} \oplus x_{ 114} \oplus x_{ 242}^6 \oplus x_{ 237}^6 \oplus x_{202}^{13} \oplus x_{ 258}^3x_{232}^7 \oplus x_{ 262}^2x_{ 246}^6 \oplus x_{228}^8x_{250}^5\\ & \quad\oplus x_{ 270}^0x_{266}^1 \oplus x_{196}^{13}x_{254}^4 \oplus x_{189}\overline{x_{59}}\oplus x_{179}x_{44} \oplus x_{270}^0x_{262}^2x_{258}^3x_{228}^8x_{196}^{13}x_{189}\end{aligned}$
16 $\begin{aligned}x_{ 153}& = z_ {16} \oplus x_{ 96} \oplus x_{ 115} \oplus x_{ 243}^6 \oplus x_{ 238}^6 \oplus x_{203}^{13} \oplus x_{ 259}^3x_{233}^7 \oplus x_{ 263}^2x_{ 247}^6 \oplus x_{229}^8x_{251}^5\\ & \quad \oplus x_{ 271}^0x_{267}^1 \oplus x_{197}^{13}x_{255}^4 \oplus x_{190}\overline{x_{60}}\oplus x_{180}x_{45} \oplus x_{271}^0x_{263}^2x_{259}^3x_{229}^8x_{197}^{13}x_{190}\end{aligned}$
17 $\begin{aligned}x_{ 154}& = z_ {17} \oplus x_{ 97} \oplus x_{ 116} \oplus x_{ 244}^6 \oplus x_{ 239}^6 \oplus x_{204}^{13} \oplus x_{ 260}^3x_{234}^7 \oplus x_{ 264}^2x_{ 248}^6 \oplus x_{230}^8x_{252}^5\\ & \quad \oplus x_{ 272}^0x_{268}^1 \oplus x_{198}^{13}x_{256}^4 \oplus x_{191}\overline{x_{61}}\oplus x_{181}\overline{x_{46}} \oplus x_{272}^0x_{264}^2x_{260}^3x_{230}^8x_{198}^{13}x_{191}\end{aligned}$
18 $\begin{aligned}x_{ 155}& = z_ {18} \oplus x_{ 98} \oplus x_{ 117} \oplus x_{ 245}^6 \oplus x_{ 240}^6 \oplus x_{205}^{13} \oplus x_{ 261}^3x_{235}^7 \oplus x_{ 265}^2x_{ 249}^6 \oplus x_{231}^8x_{253}^5\\ & \quad\oplus x_{ 273}^0x_{269}^1 \oplus x_{199}^{13}x_{257}^4 \oplus x_{192}\overline{x_{62}}\oplus x_{182}\overline{x_{47}} \oplus x_{273}^0x_{265}^2x_{261}^3x_{231}^8x_{199}^{13}x_{192}\end{aligned}$
19 $\begin{aligned}x_{ 156}& = z_ {19} \oplus x_{ 99} \oplus x_{ 118} \oplus x_{ 246}^6 \oplus x_{ 241}^6 \oplus x_{206}^{13} \oplus x_{ 262}^3x_{236}^7 \oplus x_{ 266}^2x_{ 250}^6 \oplus x_{232}^8x_{254}^5\\ & \quad \oplus x_{ 274}^0x_{270}^1 \oplus x_{200}^{13}x_{258}^4 \oplus x_{193}\overline{x_{63}}\oplus x_{183}\overline{x_{48}} \oplus x_{274}^0x_{266}^2x_{262}^3x_{232}^8x_{200}^{13}x_{193}\end{aligned}$
20 $\begin{aligned}x_{ 157}& = z_ {20} \oplus x_{100} \oplus x_{ 119} \oplus x_{ 247}^6 \oplus x_{ 242}^6 \oplus x_{207}^{13} \oplus x_{ 263}^3x_{237}^7 \oplus x_{ 267}^2x_{ 251}^6 \oplus x_{233}^8x_{255}^5\\ & \quad \oplus x_{ 275}^0x_{271}^1 \oplus x_{201}^{13}x_{259}^4 \oplus x_{194}^{13}\overline{x_{64}}\oplus x_{184}\overline{x_{49}} \oplus x_{275}^0x_{267}^2x_{263}^3x_{233}^8x_{201}^{13}x_{194}^{13}\end{aligned}$
21 $\begin{aligned}x_{ 158}& = z_ {21} \oplus x_{101} \oplus x_{ 120} \oplus x_{ 248}^6 \oplus x_{ 243}^6 \oplus x_{208}^{13} \oplus x_{ 264}^3x_{238}^7 \oplus x_{ 268}^2x_{ 252}^6 \oplus x_{234}^8x_{256}^5\\ & \quad \oplus x_{ 276}^0x_{272}^1 \oplus x_{202}^{13}x_{260}^4 \oplus x_{195}^{13}\overline{x_{65}}\oplus x_{185}\overline{x_{50}} \oplus x_{276}^0x_{268}^2x_{264}^3x_{234}^8x_{202}^{13}x_{195}^{13}\end{aligned}$
22 $\begin{aligned}x_{ 159}& = z_ {22} \oplus x_{102} \oplus x_{ 121} \oplus x_{ 249}^6 \oplus x_{ 244}^6 \oplus x_{209}^{13} \oplus x_{ 265}^3x_{239}^7 \oplus x_{ 269}^2x_{ 253}^6 \oplus x_{235}^8x_{257}^5\\ & \quad \oplus x_{ 277}^0x_{273}^1 \oplus x_{203}^{13}x_{261}^4 \oplus x_{196}^{13}\overline{x_{66}}\oplus x_{186}\overline{x_{51}} \oplus x_{277}^0x_{269}^2x_{265}^3x_{235}^8x_{203}^{13}x_{196}^{13}\end{aligned}$
23 $\begin{aligned}x_{ 160}& = z_ {23} \oplus x_{103} \oplus x_{ 122} \oplus x_{ 250}^6 \oplus x_{ 245}^6 \oplus x_{210}^{13} \oplus x_{ 266}^3x_{240}^7 \oplus x_{ 270}^2x_{ 254}^6 \oplus x_{236}^8x_{258}^5\\ & \quad \oplus x_{ 278}^0x_{274}^1 \oplus x_{204}^{13}x_{262}^4 \oplus x_{197}^{13}\overline{x_{67}}\oplus x_{187}\overline{x_{52}} \oplus x_{278}^0x_{270}^2x_{266}^3x_{236}^8x_{204}^{13}x_{197}^{13}\end{aligned}$
24 $\begin{aligned}x_{ 161}& = z_ {24} \oplus x_{104} \oplus x_{ 123} \oplus x_{ 251}^6 \oplus x_{ 246}^6 \oplus x_{211}^{13} \oplus x_{ 267}^3x_{241}^7 \oplus x_{ 271}^2x_{ 255}^6 \oplus x_{237}^8x_{259}^5\\ & \quad \oplus x_{ 279}^0x_{275}^1 \oplus x_{205}^{13}x_{263}^4 \oplus x_{198}^{13}\overline{x_{68}}\oplus x_{188}\overline{x_{53}} \oplus x_{279}^0x_{271}^2x_{267}^3x_{237}^8x_{205}^{13}x_{198}^{13} \end{aligned}$
25 $\begin{aligned}x_{ 162}& = z_ {25} \oplus x_{105} \oplus x_{ 124} \oplus x_{ 252}^6 \oplus x_{ 247}^6 \oplus x_{212}^{13} \oplus x_{ 268}^3x_{242}^7 \oplus x_{ 272}^2x_{ 256}^6 \oplus x_{238}^8x_{260}^5\\ & \quad\oplus x_{ 280}^0x_{276}^1 \oplus x_{206}^{13}x_{264}^4 \oplus x_{199}^{13}\overline{x_{69}}\oplus x_{189}\overline{x_{54}} \oplus x_{280}^0x_{272}^2x_{268}^3x_{238}^8x_{206}^{13}x_{199}^{13} \end{aligned}$
26 $\begin{aligned}x_{ 163}& = z_ {26} \oplus x_{106} \oplus x_{ 125} \oplus x_{ 253}^6 \oplus x_{ 248}^6 \oplus x_{213}^{13} \oplus x_{ 269}^3x_{243}^7 \oplus x_{ 273}^2x_{ 257}^6 \oplus x_{239}^8x_{261}^5\\ & \quad\oplus x_{ 281}^0x_{277}^1 \oplus x_{207}^{13}x_{265}^4 \oplus x_{200}^{13}\overline{x_{70}}\oplus x_{190}\overline{x_{55}} \oplus x_{281}^0x_{273}^2x_{269}^3x_{239}^8x_{207}^{13}x_{200}^{13}\end{aligned}$
27 $\begin{aligned}x_{ 164}& = z_ {27} \oplus x_{107} \oplus x_{ 126} \oplus x_{ 254}^6 \oplus x_{ 249}^6 \oplus x_{214}^{13} \oplus x_{ 270}^3x_{244}^7 \oplus x_{ 274}^2x_{ 258}^6 \oplus x_{240}^8x_{262}^5\\ & \quad\oplus x_{ 282}^0x_{278}^1 \oplus x_{208}^{13}x_{266}^4 \oplus x_{201}^{13}\overline{x_{71}}\oplus x_{191}\overline{x_{56}} \oplus x_{282}^0x_{274}^2x_{270}^3x_{240}^8x_{208}^{13}x_{201}^{13}\end{aligned}$
28 $\begin{aligned}x_{ 165}& = z_ {28} \oplus x_{108} \oplus x_{ 127} \oplus x_{ 255}^6 \oplus x_{ 250}^6 \oplus x_{215}^{13} \oplus x_{ 271}^3x_{245}^7 \oplus x_{ 275}^2x_{ 259}^6 \oplus x_{241}^8x_{263}^5\\ & \quad\oplus x_{ 283}^0x_{279}^1 \oplus x_{209}^{13}x_{267}^4 \oplus x_{202}^{13}\overline{x_{72}}\oplus x_{192}\overline{x_{57}} \oplus x_{283}^0x_{275}^2x_{271}^3x_{241}^8x_{209}^{13}x_{202}^{13}\end{aligned}$
29 $\begin{aligned}x_{ 166}& = z_ {29} \oplus x_{109} \oplus x_{ 128} \oplus x_{ 256}^6 \oplus x_{ 251}^6 \oplus x_{216}^{13} \oplus x_{ 272}^3x_{246}^7 \oplus x_{ 276}^2x_{ 260}^6 \oplus x_{242}^8x_{264}^5\\ & \quad\oplus x_{ 284}^0x_{280}^1 \oplus x_{210}^{13}x_{268}^4 \oplus x_{203}^{13}\overline{x_{73}}\oplus x_{193}\overline{x_{58}} \oplus x_{284}^0x_{276}^2x_{272}^3x_{242}^8x_{210}^{13}x_{203}^{13}\end{aligned}$
30 $\begin{aligned}x_{ 167}& = z_ {30} \oplus x_{110} \oplus x_{ 129} \oplus x_{ 257}^6 \oplus x_{ 252}^6 \oplus x_{217}^{13} \oplus x_{ 273}^3x_{247}^7 \oplus x_{ 277}^2x_{ 261}^6 \oplus x_{243}^8x_{265}^5\\ & \quad\oplus x_{ 285}^0x_{281}^1 \oplus x_{211}^{13}x_{269}^4 \oplus x_{204}^{13}\overline{x_{74}}\oplus x_{194}^{13}\overline{x_{59}} \oplus x_{285}^0x_{277}^2x_{273}^3x_{243}^8x_{211}^{13}x_{204}^{13}\end{aligned}$
31 $\begin{aligned}x_{ 168}& = z_ {31} \oplus x_{111} \oplus x_{ 130} \oplus x_{ 258}^6 \oplus x_{ 253}^6 \oplus x_{218}^{13} \oplus x_{ 274}^3x_{248}^7 \oplus x_{ 278}^2x_{ 262}^6 \oplus x_{244}^8x_{266}^5\\ & \quad\oplus x_{ 286}^0x_{282}^1 \oplus x_{212}^{13}x_{270}^4 \oplus x_{205}^{13}\overline{x_{75}}\oplus x_{195}^{13}\overline{x_{60}} \oplus x_{286}^0x_{278}^2x_{274}^3x_{244}^8x_{212}^{13}x_{205}^{13}\end{aligned}$
32 $\begin{aligned}x_{ 169}& = z_ {32} \oplus x_{112} \oplus x_{ 131} \oplus x_{ 259}^6 \oplus x_{ 254}^6 \oplus x_{219}^{13} \oplus x_{ 275}^3x_{249}^7 \oplus x_{ 279}^2x_{ 263}^6 \oplus x_{245}^8x_{267}^5\\ & \quad\oplus x_{ 287}^0x_{283}^1 \oplus x_{213}^{13}x_{271}^4 \oplus x_{206}^{13}\overline{x_{76}}\oplus x_{196}^{13}\overline{x_{61}} \oplus x_{287}^0x_{279}^2x_{275}^3x_{245}^8x_{213}^{13}x_{206}^{13}\end{aligned}$
33 $\begin{aligned}x_{170}& = z_ {33} \oplus x_{113} \oplus x_{ 132} \oplus x_{ 260}^6 \oplus x_{ 255}^6 \oplus x_{220}^{13} \oplus x_{ 276}^3x_{250}^7 \oplus x_{ 280}^2x_{ 264}^6 \oplus x_{246}^8x_{268}^5\\ & \quad\oplus x_{ 288}^0x_{284}^1 \oplus x_{214}^{13}x_{272}^4 \oplus x_{207}^{13}x_{77}\oplus x_{197}^{13}\overline{x_{62}} \oplus x_{288}^0x_{280}^2x_{276}^3x_{246}^8x_{214}^{13}x_{207}^{13}\end{aligned}$
34 $\begin{aligned} x_{171}& = z_ {34} \oplus x_{114} \oplus x_{ 133} \oplus x_{ 261}^6 \oplus x_{ 256}^6 \oplus x_{221}^{13} \oplus x_{ 277}^3x_{251}^7 \oplus x_{ 281}^2x_{ 265}^6 \oplus x_{247}^8x_{269}^5\\ & \quad\oplus x_{ 289}^0x_{285}^1 \oplus x_{215}^{13}x_{273}^4 \oplus x_{208}^{13}x_{78}\oplus x_{198}^{13}\overline{x_{63}} \oplus x_{289}^0x_{281}^2x_{277}^3x_{247}^8x_{215}^{13}x_{208}^{13}\end{aligned}$
Step/Row Equations used for recovery
0 $\begin{aligned}x_{137}& = z_ 0 \oplus x_{ 80} \oplus x_{99} \oplus x_{227} \oplus x_{222} \oplus x_{187} \oplus x_{243}x_{217} \oplus x_{247}x_{231} \oplus x_{213}x_{235} \\ & \quad \oplus x_{255}x_{251} \oplus x_{181}x_{239} \oplus x_{174}x_{44}\oplus x_{164} \overline{x_{29}} \oplus x_{255}x_{247}x_{243}x_{213}x_{181}x_{174}\end{aligned}$
1 $\begin{aligned}x_{ 138}& = z_ 1 \oplus x_{ 81} \oplus x_{ 100} \oplus x_{ 228} \oplus x_{ 223} \oplus x_{188} \oplus x_{ 244}^3x_{218}^7 \oplus x_{ 248}^2x_{ 232}^6 \oplus x_{214}^8x_{236}^5 \\ & \quad\oplus x_{ 256}^0x_{252}^1 \oplus x_{182}x_{240}^4 \oplus x_{175}x_{ 45}\oplus x_{165} \overline{x_{30}} \oplus x_{256}^0x_{248}^2x_{244}^3x_{214}^8x_{182}x_{175}\end{aligned}$
2 $\begin{aligned}x_{ 139}& = z_ 2 \oplus x_{ 82} \oplus x_{ 101} \oplus x_{ 229} \oplus x_{ 224} \oplus x_{189} \oplus x_{ 245}^3x_{219}^7 \oplus x_{ 249}^2x_{ 233}^6 \oplus x_{215}^8x_{237}^5\\ & \quad\oplus x_{ 257}^0x_{253}^1 \oplus x_{183}x_{241}^4 \oplus x_{176}\overline{x_{ 46}}\oplus x_{166} \overline{x_{31}} \oplus x_{257}^0x_{249}^2x_{245}^3x_{215}^8x_{183}x_{176}\end{aligned}$
3 $\begin{aligned}x_{ 140}& = z_ 3 \oplus x_{ 83} \oplus x_{ 102} \oplus x_{ 230} \oplus x_{ 225} \oplus x_{190} \oplus x_{ 246}^3x_{220}^7 \oplus x_{ 250}^2x_{ 234}^6 \oplus x_{216}^8x_{238}^5\\ & \quad\oplus x_{ 258}^0x_{254}^1 \oplus x_{184}x_{242}^4 \oplus x_{177}\overline{x_{ 47}}\oplus x_{167} \overline{x_{32}} \oplus x_{258}^0x_{250}^2x_{246}^3x_{216}^8x_{184}x_{177}\end{aligned}$
4 $\begin{aligned}x_{ 141}& = z_ 4 \oplus x_{ 84} \oplus x_{ 103} \oplus x_{ 231} \oplus x_{ 226} \oplus x_{191} \oplus x_{ 247}^3x_{221}^7 \oplus x_{ 251}^2x_{ 235}^6 \oplus x_{217}^8x_{239}^5\\ & \quad\oplus x_{ 259}^0x_{255}^1 \oplus x_{185}x_{243}^4 \oplus x_{178}\overline{x_{ 48}}\oplus x_{168} \overline{x_{33}} \oplus x_{259}^0x_{251}^2x_{247}^3x_{217}^8x_{185}x_{178}\end{aligned}$
5 $\begin{aligned}x_{ 142}& = z_ 5 \oplus x_{ 85} \oplus x_{ 104} \oplus x_{ 232}^6 \oplus x_{ 227} \oplus x_{192} \oplus x_{ 248}^3x_{222}^7 \oplus x_{ 252}^2x_{ 236}^6 \oplus x_{218}^8x_{240}^5\\ & \quad \oplus x_{ 260}^0x_{256}^1 \oplus x_{186}x_{244}^4 \oplus x_{179}\overline{x_{ 49}}\oplus x_{169}\overline{x_{34}} \oplus x_{260}^0x_{252}^2x_{248}^3x_{218}^8x_{186}x_{179}\end{aligned}$
6 $\begin{aligned}x_{ 143}& = z_ 6 \oplus x_{ 86} \oplus x_{ 105} \oplus x_{ 233}^6 \oplus x_{ 228} \oplus x_{193} \oplus x_{ 249}^3x_{223}^7 \oplus x_{ 253}^2x_{ 237}^6 \oplus x_{219}^8x_{241}^5\\ & \quad \oplus x_{ 261}^0x_{257}^1 \oplus x_{187}x_{245}^4 \oplus x_{180}\overline{x_{ 50}}\oplus x_{170}\overline{x_{35}} \oplus x_{261}^0x_{253}^2x_{249}^3x_{219}^8x_{187}x_{180}\end{aligned}$
7 $\begin{aligned}x_{ 144}& = z_ 7 \oplus x_{ 87} \oplus x_{ 106} \oplus x_{ 234}^6 \oplus x_{ 229} \oplus x_{194}^{13} \oplus x_{ 250}^3x_{224}^7 \oplus x_{ 254}^2x_{ 238}^6 \oplus x_{220}^8x_{242}^5\\ & \quad \oplus x_{ 262}^0x_{258}^1 \oplus x_{188}x_{246}^4 \oplus x_{181}\overline{x_{ 51}}\oplus x_{171}\overline{x_{36}} \oplus x_{262}^0x_{254}^2x_{250}^3x_{220}^8x_{188}x_{181}\end{aligned}$
8 $\begin{aligned}x_{ 145}& = z_ 8 \oplus x_{ 88} \oplus x_{ 107} \oplus x_{ 235}^6 \oplus x_{ 230} \oplus x_{195}^{13} \oplus x_{ 251}^3x_{225}^7 \oplus x_{ 255}^2x_{ 239}^6 \oplus x_{221}^8x_{243}^5\\ & \quad\oplus x_{ 263}^0x_{259}^1 \oplus x_{189}x_{247}^4 \oplus x_{182}\overline{x_{ 52}}\oplus x_{172}x_{37} \oplus x_{263}^0x_{255}^2x_{251}^3x_{221}^8x_{189}x_{182}\end{aligned}$
9 $\begin{aligned}x_{ 146}& = z_ 9 \oplus x_{ 89} \oplus x_{ 108} \oplus x_{ 236}^6 \oplus x_{ 231} \oplus x_{196}^{13} \oplus x_{ 252}^3x_{226}^7 \oplus x_{ 256}^2x_{ 240}^6 \oplus x_{222}^8x_{244}^5\\ & \quad \oplus x_{ 264}^0x_{260}^1 \oplus x_{190}x_{248}^4 \oplus x_{183}\overline{x_{ 53}}\oplus x_{173}x_{38} \oplus x_{264}^0x_{256}^2x_{252}^3x_{222}^8x_{190}x_{183}\end{aligned}$
10 $\begin{aligned}x_{ 147}& = z_ {10} \oplus x_{ 90} \oplus x_{ 109} \oplus x_{ 237}^6 \oplus x_{ 232}^6 \oplus x_{197}^{13} \oplus x_{ 253}^3x_{227}^7 \oplus x_{ 257}^2x_{ 241}^6 \oplus x_{223}^8x_{245}^5\\ & \quad\oplus x_{ 265}^0x_{261}^1 \oplus x_{191}x_{249}^4 \oplus x_{184}\overline{x_{ 54}}\oplus x_{174}x_{39} \oplus x_{265}^0x_{257}^2x_{253}^3x_{223}^8x_{191}x_{184}\end{aligned}$
11 $\begin{aligned}x_{ 148}& = z_ {11} \oplus x_{ 91} \oplus x_{ 110} \oplus x_{ 238}^6 \oplus x_{ 233}^6 \oplus x_{198}^{13} \oplus x_{ 254}^3x_{228}^7 \oplus x_{ 258}^2x_{ 242}^6 \oplus x_{224}^8x_{246}^5\\ & \quad \oplus x_{ 266}^0x_{262}^1 \oplus x_{192}x_{250}^4 \oplus x_{185}\overline{x_{ 55}}\oplus x_{175}x_{40} \oplus x_{266}^0x_{258}^2x_{254}^3x_{224}^8x_{192}x_{185}\end{aligned}$
12 $\begin{aligned}x_{ 149}& = z_ {12} \oplus x_{ 92} \oplus x_{ 111} \oplus x_{ 239}^6 \oplus x_{ 234}^6 \oplus x_{199}^{13} \oplus x_{ 255}^3x_{229}^7 \oplus x_{ 259}^2x_{ 243}^6 \oplus x_{225}^8x_{247}^5\\ & \quad\oplus x_{ 267}^0x_{263}^1 \oplus x_{193}x_{251}^4 \oplus x_{186}\overline{x_{ 56}}\oplus x_{176}x_{41} \oplus x_{267}^0x_{259}^2x_{255}^3x_{225}^8x_{193}x_{186}\end{aligned}$
13 $\begin{aligned}x_{ 150}& = z_ {13} \oplus x_{ 93} \oplus x_{ 112} \oplus x_{ 240}^6 \oplus x_{ 235}^6 \oplus x_{200}^{13} \oplus x_{ 256}^3x_{230}^7 \oplus x_{ 260}^2x_{ 244}^6 \oplus x_{226}^8x_{248}^5\\ & \quad\oplus x_{ 268}^0x_{264}^1 \oplus x_{194}^{13}x_{252}^4 \oplus x_{187}\overline{x_{ 57}}\oplus x_{177}x_{42} \oplus x_{268}^0x_{260}^2x_{256}^3x_{226}^8x_{194}^{13}x_{187}\end{aligned}$
14 $\begin{aligned}x_{ 151}& = z_ {14} \oplus x_{ 94} \oplus x_{ 113} \oplus x_{ 241}^6 \oplus x_{ 236}^6 \oplus x_{201}^{13} \oplus x_{ 257}^3x_{231}^7 \oplus x_{ 261}^2x_{ 245}^6 \oplus x_{227}^8x_{249}^5\\ & \quad\oplus x_{ 269}^0x_{265}^1 \oplus x_{195}^{13}x_{253}^4 \oplus x_{188}\overline{x_{ 58}}\oplus x_{178}x_{43} \oplus x_{269}^0x_{261}^2x_{257}^3x_{227}^8x_{195}^{13}x_{188}\end{aligned}$
15 $\begin{aligned}x_{ 152}& = z_ {15} \oplus x_{ 95} \oplus x_{ 114} \oplus x_{ 242}^6 \oplus x_{ 237}^6 \oplus x_{202}^{13} \oplus x_{ 258}^3x_{232}^7 \oplus x_{ 262}^2x_{ 246}^6 \oplus x_{228}^8x_{250}^5\\ & \quad\oplus x_{ 270}^0x_{266}^1 \oplus x_{196}^{13}x_{254}^4 \oplus x_{189}\overline{x_{59}}\oplus x_{179}x_{44} \oplus x_{270}^0x_{262}^2x_{258}^3x_{228}^8x_{196}^{13}x_{189}\end{aligned}$
16 $\begin{aligned}x_{ 153}& = z_ {16} \oplus x_{ 96} \oplus x_{ 115} \oplus x_{ 243}^6 \oplus x_{ 238}^6 \oplus x_{203}^{13} \oplus x_{ 259}^3x_{233}^7 \oplus x_{ 263}^2x_{ 247}^6 \oplus x_{229}^8x_{251}^5\\ & \quad \oplus x_{ 271}^0x_{267}^1 \oplus x_{197}^{13}x_{255}^4 \oplus x_{190}\overline{x_{60}}\oplus x_{180}x_{45} \oplus x_{271}^0x_{263}^2x_{259}^3x_{229}^8x_{197}^{13}x_{190}\end{aligned}$
17 $\begin{aligned}x_{ 154}& = z_ {17} \oplus x_{ 97} \oplus x_{ 116} \oplus x_{ 244}^6 \oplus x_{ 239}^6 \oplus x_{204}^{13} \oplus x_{ 260}^3x_{234}^7 \oplus x_{ 264}^2x_{ 248}^6 \oplus x_{230}^8x_{252}^5\\ & \quad \oplus x_{ 272}^0x_{268}^1 \oplus x_{198}^{13}x_{256}^4 \oplus x_{191}\overline{x_{61}}\oplus x_{181}\overline{x_{46}} \oplus x_{272}^0x_{264}^2x_{260}^3x_{230}^8x_{198}^{13}x_{191}\end{aligned}$
18 $\begin{aligned}x_{ 155}& = z_ {18} \oplus x_{ 98} \oplus x_{ 117} \oplus x_{ 245}^6 \oplus x_{ 240}^6 \oplus x_{205}^{13} \oplus x_{ 261}^3x_{235}^7 \oplus x_{ 265}^2x_{ 249}^6 \oplus x_{231}^8x_{253}^5\\ & \quad\oplus x_{ 273}^0x_{269}^1 \oplus x_{199}^{13}x_{257}^4 \oplus x_{192}\overline{x_{62}}\oplus x_{182}\overline{x_{47}} \oplus x_{273}^0x_{265}^2x_{261}^3x_{231}^8x_{199}^{13}x_{192}\end{aligned}$
19 $\begin{aligned}x_{ 156}& = z_ {19} \oplus x_{ 99} \oplus x_{ 118} \oplus x_{ 246}^6 \oplus x_{ 241}^6 \oplus x_{206}^{13} \oplus x_{ 262}^3x_{236}^7 \oplus x_{ 266}^2x_{ 250}^6 \oplus x_{232}^8x_{254}^5\\ & \quad \oplus x_{ 274}^0x_{270}^1 \oplus x_{200}^{13}x_{258}^4 \oplus x_{193}\overline{x_{63}}\oplus x_{183}\overline{x_{48}} \oplus x_{274}^0x_{266}^2x_{262}^3x_{232}^8x_{200}^{13}x_{193}\end{aligned}$
20 $\begin{aligned}x_{ 157}& = z_ {20} \oplus x_{100} \oplus x_{ 119} \oplus x_{ 247}^6 \oplus x_{ 242}^6 \oplus x_{207}^{13} \oplus x_{ 263}^3x_{237}^7 \oplus x_{ 267}^2x_{ 251}^6 \oplus x_{233}^8x_{255}^5\\ & \quad \oplus x_{ 275}^0x_{271}^1 \oplus x_{201}^{13}x_{259}^4 \oplus x_{194}^{13}\overline{x_{64}}\oplus x_{184}\overline{x_{49}} \oplus x_{275}^0x_{267}^2x_{263}^3x_{233}^8x_{201}^{13}x_{194}^{13}\end{aligned}$
21 $\begin{aligned}x_{ 158}& = z_ {21} \oplus x_{101} \oplus x_{ 120} \oplus x_{ 248}^6 \oplus x_{ 243}^6 \oplus x_{208}^{13} \oplus x_{ 264}^3x_{238}^7 \oplus x_{ 268}^2x_{ 252}^6 \oplus x_{234}^8x_{256}^5\\ & \quad \oplus x_{ 276}^0x_{272}^1 \oplus x_{202}^{13}x_{260}^4 \oplus x_{195}^{13}\overline{x_{65}}\oplus x_{185}\overline{x_{50}} \oplus x_{276}^0x_{268}^2x_{264}^3x_{234}^8x_{202}^{13}x_{195}^{13}\end{aligned}$
22 $\begin{aligned}x_{ 159}& = z_ {22} \oplus x_{102} \oplus x_{ 121} \oplus x_{ 249}^6 \oplus x_{ 244}^6 \oplus x_{209}^{13} \oplus x_{ 265}^3x_{239}^7 \oplus x_{ 269}^2x_{ 253}^6 \oplus x_{235}^8x_{257}^5\\ & \quad \oplus x_{ 277}^0x_{273}^1 \oplus x_{203}^{13}x_{261}^4 \oplus x_{196}^{13}\overline{x_{66}}\oplus x_{186}\overline{x_{51}} \oplus x_{277}^0x_{269}^2x_{265}^3x_{235}^8x_{203}^{13}x_{196}^{13}\end{aligned}$
23 $\begin{aligned}x_{ 160}& = z_ {23} \oplus x_{103} \oplus x_{ 122} \oplus x_{ 250}^6 \oplus x_{ 245}^6 \oplus x_{210}^{13} \oplus x_{ 266}^3x_{240}^7 \oplus x_{ 270}^2x_{ 254}^6 \oplus x_{236}^8x_{258}^5\\ & \quad \oplus x_{ 278}^0x_{274}^1 \oplus x_{204}^{13}x_{262}^4 \oplus x_{197}^{13}\overline{x_{67}}\oplus x_{187}\overline{x_{52}} \oplus x_{278}^0x_{270}^2x_{266}^3x_{236}^8x_{204}^{13}x_{197}^{13}\end{aligned}$
24 $\begin{aligned}x_{ 161}& = z_ {24} \oplus x_{104} \oplus x_{ 123} \oplus x_{ 251}^6 \oplus x_{ 246}^6 \oplus x_{211}^{13} \oplus x_{ 267}^3x_{241}^7 \oplus x_{ 271}^2x_{ 255}^6 \oplus x_{237}^8x_{259}^5\\ & \quad \oplus x_{ 279}^0x_{275}^1 \oplus x_{205}^{13}x_{263}^4 \oplus x_{198}^{13}\overline{x_{68}}\oplus x_{188}\overline{x_{53}} \oplus x_{279}^0x_{271}^2x_{267}^3x_{237}^8x_{205}^{13}x_{198}^{13} \end{aligned}$
25 $\begin{aligned}x_{ 162}& = z_ {25} \oplus x_{105} \oplus x_{ 124} \oplus x_{ 252}^6 \oplus x_{ 247}^6 \oplus x_{212}^{13} \oplus x_{ 268}^3x_{242}^7 \oplus x_{ 272}^2x_{ 256}^6 \oplus x_{238}^8x_{260}^5\\ & \quad\oplus x_{ 280}^0x_{276}^1 \oplus x_{206}^{13}x_{264}^4 \oplus x_{199}^{13}\overline{x_{69}}\oplus x_{189}\overline{x_{54}} \oplus x_{280}^0x_{272}^2x_{268}^3x_{238}^8x_{206}^{13}x_{199}^{13} \end{aligned}$
26 $\begin{aligned}x_{ 163}& = z_ {26} \oplus x_{106} \oplus x_{ 125} \oplus x_{ 253}^6 \oplus x_{ 248}^6 \oplus x_{213}^{13} \oplus x_{ 269}^3x_{243}^7 \oplus x_{ 273}^2x_{ 257}^6 \oplus x_{239}^8x_{261}^5\\ & \quad\oplus x_{ 281}^0x_{277}^1 \oplus x_{207}^{13}x_{265}^4 \oplus x_{200}^{13}\overline{x_{70}}\oplus x_{190}\overline{x_{55}} \oplus x_{281}^0x_{273}^2x_{269}^3x_{239}^8x_{207}^{13}x_{200}^{13}\end{aligned}$
27 $\begin{aligned}x_{ 164}& = z_ {27} \oplus x_{107} \oplus x_{ 126} \oplus x_{ 254}^6 \oplus x_{ 249}^6 \oplus x_{214}^{13} \oplus x_{ 270}^3x_{244}^7 \oplus x_{ 274}^2x_{ 258}^6 \oplus x_{240}^8x_{262}^5\\ & \quad\oplus x_{ 282}^0x_{278}^1 \oplus x_{208}^{13}x_{266}^4 \oplus x_{201}^{13}\overline{x_{71}}\oplus x_{191}\overline{x_{56}} \oplus x_{282}^0x_{274}^2x_{270}^3x_{240}^8x_{208}^{13}x_{201}^{13}\end{aligned}$
28 $\begin{aligned}x_{ 165}& = z_ {28} \oplus x_{108} \oplus x_{ 127} \oplus x_{ 255}^6 \oplus x_{ 250}^6 \oplus x_{215}^{13} \oplus x_{ 271}^3x_{245}^7 \oplus x_{ 275}^2x_{ 259}^6 \oplus x_{241}^8x_{263}^5\\ & \quad\oplus x_{ 283}^0x_{279}^1 \oplus x_{209}^{13}x_{267}^4 \oplus x_{202}^{13}\overline{x_{72}}\oplus x_{192}\overline{x_{57}} \oplus x_{283}^0x_{275}^2x_{271}^3x_{241}^8x_{209}^{13}x_{202}^{13}\end{aligned}$
29 $\begin{aligned}x_{ 166}& = z_ {29} \oplus x_{109} \oplus x_{ 128} \oplus x_{ 256}^6 \oplus x_{ 251}^6 \oplus x_{216}^{13} \oplus x_{ 272}^3x_{246}^7 \oplus x_{ 276}^2x_{ 260}^6 \oplus x_{242}^8x_{264}^5\\ & \quad\oplus x_{ 284}^0x_{280}^1 \oplus x_{210}^{13}x_{268}^4 \oplus x_{203}^{13}\overline{x_{73}}\oplus x_{193}\overline{x_{58}} \oplus x_{284}^0x_{276}^2x_{272}^3x_{242}^8x_{210}^{13}x_{203}^{13}\end{aligned}$
30 $\begin{aligned}x_{ 167}& = z_ {30} \oplus x_{110} \oplus x_{ 129} \oplus x_{ 257}^6 \oplus x_{ 252}^6 \oplus x_{217}^{13} \oplus x_{ 273}^3x_{247}^7 \oplus x_{ 277}^2x_{ 261}^6 \oplus x_{243}^8x_{265}^5\\ & \quad\oplus x_{ 285}^0x_{281}^1 \oplus x_{211}^{13}x_{269}^4 \oplus x_{204}^{13}\overline{x_{74}}\oplus x_{194}^{13}\overline{x_{59}} \oplus x_{285}^0x_{277}^2x_{273}^3x_{243}^8x_{211}^{13}x_{204}^{13}\end{aligned}$
31 $\begin{aligned}x_{ 168}& = z_ {31} \oplus x_{111} \oplus x_{ 130} \oplus x_{ 258}^6 \oplus x_{ 253}^6 \oplus x_{218}^{13} \oplus x_{ 274}^3x_{248}^7 \oplus x_{ 278}^2x_{ 262}^6 \oplus x_{244}^8x_{266}^5\\ & \quad\oplus x_{ 286}^0x_{282}^1 \oplus x_{212}^{13}x_{270}^4 \oplus x_{205}^{13}\overline{x_{75}}\oplus x_{195}^{13}\overline{x_{60}} \oplus x_{286}^0x_{278}^2x_{274}^3x_{244}^8x_{212}^{13}x_{205}^{13}\end{aligned}$
32 $\begin{aligned}x_{ 169}& = z_ {32} \oplus x_{112} \oplus x_{ 131} \oplus x_{ 259}^6 \oplus x_{ 254}^6 \oplus x_{219}^{13} \oplus x_{ 275}^3x_{249}^7 \oplus x_{ 279}^2x_{ 263}^6 \oplus x_{245}^8x_{267}^5\\ & \quad\oplus x_{ 287}^0x_{283}^1 \oplus x_{213}^{13}x_{271}^4 \oplus x_{206}^{13}\overline{x_{76}}\oplus x_{196}^{13}\overline{x_{61}} \oplus x_{287}^0x_{279}^2x_{275}^3x_{245}^8x_{213}^{13}x_{206}^{13}\end{aligned}$
33 $\begin{aligned}x_{170}& = z_ {33} \oplus x_{113} \oplus x_{ 132} \oplus x_{ 260}^6 \oplus x_{ 255}^6 \oplus x_{220}^{13} \oplus x_{ 276}^3x_{250}^7 \oplus x_{ 280}^2x_{ 264}^6 \oplus x_{246}^8x_{268}^5\\ & \quad\oplus x_{ 288}^0x_{284}^1 \oplus x_{214}^{13}x_{272}^4 \oplus x_{207}^{13}x_{77}\oplus x_{197}^{13}\overline{x_{62}} \oplus x_{288}^0x_{280}^2x_{276}^3x_{246}^8x_{214}^{13}x_{207}^{13}\end{aligned}$
34 $\begin{aligned} x_{171}& = z_ {34} \oplus x_{114} \oplus x_{ 133} \oplus x_{ 261}^6 \oplus x_{ 256}^6 \oplus x_{221}^{13} \oplus x_{ 277}^3x_{251}^7 \oplus x_{ 281}^2x_{ 265}^6 \oplus x_{247}^8x_{269}^5\\ & \quad\oplus x_{ 289}^0x_{285}^1 \oplus x_{215}^{13}x_{273}^4 \oplus x_{208}^{13}x_{78}\oplus x_{198}^{13}\overline{x_{63}} \oplus x_{289}^0x_{281}^2x_{277}^3x_{247}^8x_{215}^{13}x_{208}^{13}\end{aligned}$
Table 5.  Possible tradeoffs for conditional BSW sampling resistance based TMDTO attack
$ \delta $ $ D' $ $ T' $ $ M $ $ P $
$ 30 $ $ 2^{104} $ $ 2^{99} $ $ 2^{122} $ $ 2^{152} $
$ 32 $ $ 2^{106} $ $ 2^{103} $ $ 2^{118} $ $ 2^{150} $
$ 34 $ $ 2^{108} $ $ 2^{107} $ $ 2^{114} $ $ 2^{148} $
$ \delta $ $ D' $ $ T' $ $ M $ $ P $
$ 30 $ $ 2^{104} $ $ 2^{99} $ $ 2^{122} $ $ 2^{152} $
$ 32 $ $ 2^{106} $ $ 2^{103} $ $ 2^{118} $ $ 2^{150} $
$ 34 $ $ 2^{108} $ $ 2^{107} $ $ 2^{114} $ $ 2^{148} $
[1]

Anupama N, Sudarson Jena. A novel approach using incremental under sampling for data stream mining. Big Data & Information Analytics, 2018  doi: 10.3934/bdia.2017017

[2]

Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227

[3]

Ke Xu, M. Gregory Forest, Xiaofeng Yang. Shearing the I-N phase transition of liquid crystalline polymers: Long-time memory of defect initial data. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 457-473. doi: 10.3934/dcdsb.2011.15.457

[4]

Vincent Astier, Thomas Unger. Galois extensions, positive involutions and an application to unitary space-time coding. Advances in Mathematics of Communications, 2019, 13 (3) : 513-516. doi: 10.3934/amc.2019032

[5]

Jingzhi Li, Jun Zou. A direct sampling method for inverse scattering using far-field data. Inverse Problems & Imaging, 2013, 7 (3) : 757-775. doi: 10.3934/ipi.2013.7.757

[6]

Christopher Rackauckas, Qing Nie. Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2731-2761. doi: 10.3934/dcdsb.2017133

[7]

David Grant, Mahesh K. Varanasi. The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications, 2008, 2 (2) : 131-145. doi: 10.3934/amc.2008.2.131

[8]

Hiroshi Nishiura. Time variations in the generation time of an infectious disease: Implications for sampling to appropriately quantify transmission potential. Mathematical Biosciences & Engineering, 2010, 7 (4) : 851-869. doi: 10.3934/mbe.2010.7.851

[9]

Joan-Josep Climent, Elisa Gorla, Joachim Rosenthal. Cryptanalysis of the CFVZ cryptosystem. Advances in Mathematics of Communications, 2007, 1 (1) : 1-11. doi: 10.3934/amc.2007.1.1

[10]

Jáuber Cavalcante Oliveira, Jardel Morais Pereira, Gustavo Perla Menzala. Long time dynamics of a multidimensional nonlinear lattice with memory. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2715-2732. doi: 10.3934/dcdsb.2015.20.2715

[11]

Giacomo Micheli. Cryptanalysis of a noncommutative key exchange protocol. Advances in Mathematics of Communications, 2015, 9 (2) : 247-253. doi: 10.3934/amc.2015.9.247

[12]

Victor Zvyagin, Vladimir Orlov. On one problem of viscoelastic fluid dynamics with memory on an infinite time interval. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3855-3877. doi: 10.3934/dcdsb.2018114

[13]

Tingting Liu, Qiaozhen Ma. Time-dependent asymptotic behavior of the solution for plate equations with linear memory. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4595-4616. doi: 10.3934/dcdsb.2018178

[14]

Jiao Song, Jiang-Lun Wu, Fangzhou Huang. First jump time in simulation of sampling trajectories of affine jump-diffusions driven by $ \alpha $-stable white noise. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4127-4142. doi: 10.3934/cpaa.2020184

[15]

Ruediger Landes. Stable and unstable initial configuration in the theory wave fronts. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 797-808. doi: 10.3934/dcdss.2012.5.797

[16]

Subhabrata Samajder, Palash Sarkar. Another look at success probability of linear cryptanalysis. Advances in Mathematics of Communications, 2019, 13 (4) : 645-688. doi: 10.3934/amc.2019040

[17]

Keaton Hamm, Longxiu Huang. Stability of sampling for CUR decompositions. Foundations of Data Science, 2020, 2 (2) : 83-99. doi: 10.3934/fods.2020006

[18]

Claude Carlet, Juan Carlos Ku-Cauich, Horacio Tapia-Recillas. Bent functions on a Galois ring and systematic authentication codes. Advances in Mathematics of Communications, 2012, 6 (2) : 249-258. doi: 10.3934/amc.2012.6.249

[19]

Delphine Boucher, Patrick Solé, Felix Ulmer. Skew constacyclic codes over Galois rings. Advances in Mathematics of Communications, 2008, 2 (3) : 273-292. doi: 10.3934/amc.2008.2.273

[20]

Timothy C. Reluga, Jan Medlock. Resistance mechanisms matter in SIR models. Mathematical Biosciences & Engineering, 2007, 4 (3) : 553-563. doi: 10.3934/mbe.2007.4.553

2019 Impact Factor: 0.734

Metrics

  • PDF downloads (57)
  • HTML views (282)
  • Cited by (0)

Other articles
by authors

[Back to Top]