# American Institute of Mathematical Sciences

August  2021, 15(3): 539-556. 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, 2021, 15 (3) : 539-556. 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. Biryukov, A. 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. Hell, T. Johansson, A. 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. Maitra, N. Sinha, A. Siddhanti, R. 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. Mihaljević, S. Gangopadhyay, G. 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. Mihaljević, S. Gangopadhyay, G. 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

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##### 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. Biryukov, A. 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. Hell, T. Johansson, A. 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. Maitra, N. Sinha, A. Siddhanti, R. 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. Mihaljević, S. Gangopadhyay, G. 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. Mihaljević, S. Gangopadhyay, G. 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
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 $x_{290}^0$ $x_{34}, \overline{x_{75}}, \underline{x_{104}}$ $x_{286}^1$ $\underline{x_{286}^0}, \overline{x_{76}},$ $\underline{x_{117}}, x_{42}$ $x_{282}^2$ $x_{282}^1, x_{78},$ $x_{136}, \overline{x_{74}}$ $x_{278}^3$ $x_{278}^2, x_{77},$ $x_{152}, x_{137}$ $x_{274}^4$ $x_{274}^3, x_{80},$ $x_{175}, x_{151}$
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 $x_{270}^5$ $x_{270}^4, x_{101}, x_{124}, x_{144}, x_{171}$ $x_{266}^6$ $x_{266}^5, x_{84},$ $x_{193}, x_{223}^{13}$ $x_{252}^7$ $x_{252}^6, \underline{x_{37}}, \overline{x_{66}}$ $x_{248}^8$ $x_{248}^7, x_{38}, x_{79}$ $x_{244}^9$ $x_{244}^8, x_{40}, x_{98}$
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 $x_{240}^{10}$ $x_{240}^9, x_{39}, x_{114}$ $x_{236}^{11}$ $x_{236}^{10}, x_{42},$ $x_{137}$ $x_{232}^{12}$ $x_{232}^{11}, \overline{x_{63}}, \underline{x_{86}}, \underline{x_{106}}, \underline{x_{133}}$ $x_{228}^{13}$ $x_{228}^{12}, \overline{x_{46}}, \underline{x_{155}}$
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}
Possible tradeoffs for conditional BSW sampling resistance based TMDTO attack
 $\delta$ $D'$ $T'$ $M$ $P$ $30$ $2^{104}$ $2^{99}$ $2^{122}$ $2^{152}$ $32$ $2^{106}$ $2^{103}$ $2^{118}$ $2^{150}$ $34$ $2^{108}$ $2^{107}$ $2^{114}$ $2^{148}$
 $\delta$ $D'$ $T'$ $M$ $P$ $30$ $2^{104}$ $2^{99}$ $2^{122}$ $2^{152}$ $32$ $2^{106}$ $2^{103}$ $2^{118}$ $2^{150}$ $34$ $2^{108}$ $2^{107}$ $2^{114}$ $2^{148}$
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