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Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes
Self-dual codes with an automorphism of order 13
1. | Faculty of Mathematics and Informatics, Shumen University, 9700 Shumen, Bulgaria |
2. | Istanbul Aydin University, Istanbul, Turkey |
Using a method for constructing binary self-dual codes having an automorphism of odd prime order $p$ we classify, up to equivalence, all singly-even self-dual $[78,39,14]$, $[80,40,14]$, $[82,41,14],$ and $[84,42,14]$ codes as well as all doubly-even $[80,40,16]$ codes for $p=13$. The results show that there are exactly 1592 inequivalent binary self-dual $[78,39,14]$ codes with an automorphism of type $13-(6,0)$ and we found 6 new values of the parameter in the weight function thus increasing more than twice the number of known values. As for binary $[80,40]$ self-dual codes with an automorphism of type $13-(6,2)$ there are 162696 singly-even self-dual codes with minimum distance 14 and 195 doubly-even such codes with minimum distance 16. We also construct many new codes of lengths 82 and 84 with minimum distance 14. Most of the constructed codes for all lengths have weight enumerators for which the existence was not known before.
References:
[1] |
A. Baartmans and V. Yorgov,
Some new extremal codes of lengths 76 and 78, IEEE Trans. Inf. Theory, 49 (2003), 1353-1354.
doi: 10.1109/tit.2003.810653. |
[2] |
I. Bouyukliev, About the code equivalence, in Advances in Coding Theory and Cryptography,
World Scient. Publ. Comp. , 2007,126–151.
doi: 10.1142/9789812772022_0009. |
[3] |
R. Dontcheva and M. Harada,
Extremal doubly-even [80, 40, 16] codes with an automorphism of order 19, Finite Fields Appl., 9 (2003), 157-167.
doi: 10.1016/s1071-5797(02)00018-7. |
[4] |
G. Dorfer and H. Maharaj,
Generalized AG codes and generalized duality, Finite Fields Appl., 9 (2003), 194-210.
doi: 10.1016/s1071-5797(02)00027-8. |
[5] |
S. T. Dougherty, T. A. Gulliver and M. Harada,
Extremal binary self-dual codes, IEEE Trans. Inf. Theory, 43 (1997), 2036-2047.
doi: 10.1109/18.641574. |
[6] |
P. Gaborit and A. Otmani,
Experimental constructions of self-dual codes, Finite Fields Appl., 9 (2003), 372-394.
doi: 10.1016/s1071-5797(03)00011-x. |
[7] |
The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4. 8. 6,2016, http://www.gap-system.org |
[8] |
T. A. Gulliver and M. Harada,
Classification of extremal double circulant self-dual codes of lengths 74–88, Discr. Math., 306 (2006), 2064-2072.
doi: 10.1016/j.disc.2006.05.004. |
[9] |
T. A. Gulliver, M. Harada and J.-L. Kim,
Construction of new extremal self-dual codes, Discr. Math., 263 (2003), 81-91.
doi: 10.1016/s0012-365x(02)00570-8. |
[10] |
M. Harada and A. Munemasa,
On $s$-extremal singly even self-dual $[24k+8, 12k+4, 4k+2]$ codes preprint, arXiv: 1511.02972 |
[11] |
M. Harada and A. Munemasa,
Some restrictions on weight enumerators of singly even self-dual codes, IEEE Trans. Inf. Theory, 52 (2006), 1266-1269.
doi: 10.1109/tit.2005.864416. |
[12] |
W. C. Huffman,
Automorphisms of codes with applications to extremal doubly even codes of length 48, IEEE Trans. Inf. Theory, 28 (1982), 511-521.
doi: 10.1109/tit.1982.1056499. |
[13] |
W. C. Huffman and V. S. Pless,
Fundamentals of Error-Correcting Codes Cambridge Univ. Press, 2003.
doi: 10.1017/CBO9780511807077. |
[14] |
S. Kapralov, R. Russeva and V. Radeva, New extremal doubly even [80, 40, 16] codes with
an automorphism of order 13, in Proc. 8th Int. Workshop Algebr. Combin. Coding Theory,
2002,139–142. |
[15] |
E. Rains,
Shadow bounds for self-dual codes, IEEE Trans. Inf. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[16] |
N. Yankov,
Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7, Adv. Math. Commun., 8 (2014), 73-81.
doi: 10.3934/amc.2014.8.73. |
[17] |
N. Yankov, D. Anev and M. Gürel,
Constructing the self-dual codes with an automorphism of order 13 with 6 cycles available at http://shu.bg/tadmin/upload/storage/2497.pdf |
[18] |
N. Yankov and M. H. Lee,
Classification of self-dual codes of length 50 with an automorphism of odd prime order, Des. Codes Crypt., 74 (2015), 571-579.
doi: 10.1007/s10623-013-9874-8. |
[19] |
N. Yankov and R. Russeva,
Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13, IEEE Trans. Inf. Theory, 57 (2011), 7498-7506.
doi: 10.1109/TIT.2011.2155619. |
[20] |
V. Yorgov,
Binary self-dual codes with automorphisms of odd order, Probl. Inf. Transm., 19 (1983), 260-270.
|
[21] |
V. Yorgov,
A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inf. Theory, 33 (1987), 77-82.
doi: 10.1109/TIT.1987.1057273. |
[22] |
T. Zhang, J. Michel, T. Feng and G. Ge,
On the existence of certain optimal self-dual codes with lengths between 74 and 116 Electr. J. Combin. 22 (2015), P4. 33. |
show all references
References:
[1] |
A. Baartmans and V. Yorgov,
Some new extremal codes of lengths 76 and 78, IEEE Trans. Inf. Theory, 49 (2003), 1353-1354.
doi: 10.1109/tit.2003.810653. |
[2] |
I. Bouyukliev, About the code equivalence, in Advances in Coding Theory and Cryptography,
World Scient. Publ. Comp. , 2007,126–151.
doi: 10.1142/9789812772022_0009. |
[3] |
R. Dontcheva and M. Harada,
Extremal doubly-even [80, 40, 16] codes with an automorphism of order 19, Finite Fields Appl., 9 (2003), 157-167.
doi: 10.1016/s1071-5797(02)00018-7. |
[4] |
G. Dorfer and H. Maharaj,
Generalized AG codes and generalized duality, Finite Fields Appl., 9 (2003), 194-210.
doi: 10.1016/s1071-5797(02)00027-8. |
[5] |
S. T. Dougherty, T. A. Gulliver and M. Harada,
Extremal binary self-dual codes, IEEE Trans. Inf. Theory, 43 (1997), 2036-2047.
doi: 10.1109/18.641574. |
[6] |
P. Gaborit and A. Otmani,
Experimental constructions of self-dual codes, Finite Fields Appl., 9 (2003), 372-394.
doi: 10.1016/s1071-5797(03)00011-x. |
[7] |
The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4. 8. 6,2016, http://www.gap-system.org |
[8] |
T. A. Gulliver and M. Harada,
Classification of extremal double circulant self-dual codes of lengths 74–88, Discr. Math., 306 (2006), 2064-2072.
doi: 10.1016/j.disc.2006.05.004. |
[9] |
T. A. Gulliver, M. Harada and J.-L. Kim,
Construction of new extremal self-dual codes, Discr. Math., 263 (2003), 81-91.
doi: 10.1016/s0012-365x(02)00570-8. |
[10] |
M. Harada and A. Munemasa,
On $s$-extremal singly even self-dual $[24k+8, 12k+4, 4k+2]$ codes preprint, arXiv: 1511.02972 |
[11] |
M. Harada and A. Munemasa,
Some restrictions on weight enumerators of singly even self-dual codes, IEEE Trans. Inf. Theory, 52 (2006), 1266-1269.
doi: 10.1109/tit.2005.864416. |
[12] |
W. C. Huffman,
Automorphisms of codes with applications to extremal doubly even codes of length 48, IEEE Trans. Inf. Theory, 28 (1982), 511-521.
doi: 10.1109/tit.1982.1056499. |
[13] |
W. C. Huffman and V. S. Pless,
Fundamentals of Error-Correcting Codes Cambridge Univ. Press, 2003.
doi: 10.1017/CBO9780511807077. |
[14] |
S. Kapralov, R. Russeva and V. Radeva, New extremal doubly even [80, 40, 16] codes with
an automorphism of order 13, in Proc. 8th Int. Workshop Algebr. Combin. Coding Theory,
2002,139–142. |
[15] |
E. Rains,
Shadow bounds for self-dual codes, IEEE Trans. Inf. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[16] |
N. Yankov,
Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7, Adv. Math. Commun., 8 (2014), 73-81.
doi: 10.3934/amc.2014.8.73. |
[17] |
N. Yankov, D. Anev and M. Gürel,
Constructing the self-dual codes with an automorphism of order 13 with 6 cycles available at http://shu.bg/tadmin/upload/storage/2497.pdf |
[18] |
N. Yankov and M. H. Lee,
Classification of self-dual codes of length 50 with an automorphism of odd prime order, Des. Codes Crypt., 74 (2015), 571-579.
doi: 10.1007/s10623-013-9874-8. |
[19] |
N. Yankov and R. Russeva,
Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13, IEEE Trans. Inf. Theory, 57 (2011), 7498-7506.
doi: 10.1109/TIT.2011.2155619. |
[20] |
V. Yorgov,
Binary self-dual codes with automorphisms of odd order, Probl. Inf. Transm., 19 (1983), 260-270.
|
[21] |
V. Yorgov,
A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inf. Theory, 33 (1987), 77-82.
doi: 10.1109/TIT.1987.1057273. |
[22] |
T. Zhang, J. Michel, T. Feng and G. Ge,
On the existence of certain optimal self-dual codes with lengths between 74 and 116 Electr. J. Combin. 22 (2015), P4. 33. |
# | # | # | # | # | # | # | # | ||||||||
14586 | 1 | 15002 | 359 | 15379 | 4280 | 15756 | 4993 | 16133 | 1458 | 16510 | 189 | 16887 | 16 | 17290 | 3 |
14612 | 1 | 15015 | 417 | 15392 | 4282 | 15769 | 4803 | 16146 | 1381 | 16523 | 144 | 16900 | 11 | 17303 | 4 |
14625 | 2 | 15028 | 528 | 15405 | 4380 | 15782 | 4902 | 16159 | 1198 | 16536 | 140 | 16913 | 11 | 17316 | 2 |
14651 | 1 | 15041 | 539 | 15418 | 4551 | 15795 | 4669 | 16172 | 1089 | 16549 | 144 | 16926 | 14 | 17342 | 1 |
14677 | 4 | 15054 | 608 | 15431 | 4766 | 15808 | 4414 | 16185 | 1111 | 16562 | 136 | 16939 | 11 | 17368 | 2 |
14690 | 1 | 15067 | 707 | 15444 | 4805 | 15821 | 4425 | 16198 | 1077 | 16575 | 113 | 16952 | 6 | 17394 | 2 |
14703 | 2 | 15080 | 735 | 15457 | 4842 | 15834 | 4215 | 16211 | 1007 | 16588 | 101 | 16965 | 12 | 17407 | 1 |
14716 | 3 | 15093 | 870 | 15470 | 5185 | 15847 | 4008 | 16224 | 856 | 16601 | 90 | 16978 | 7 | 17420 | 1 |
14729 | 9 | 15106 | 957 | 15483 | 5164 | 15860 | 3988 | 16237 | 876 | 16614 | 88 | 16991 | 7 | 17433 | 1 |
14742 | 4 | 15119 | 1031 | 15496 | 5366 | 15873 | 3865 | 16250 | 767 | 16627 | 70 | 17004 | 4 | 17446 | 3 |
14755 | 6 | 15132 | 1176 | 15509 | 5393 | 15886 | 3854 | 16263 | 762 | 16640 | 83 | 17017 | 3 | 17472 | 2 |
14768 | 8 | 15145 | 1277 | 15522 | 5480 | 15899 | 3611 | 16276 | 706 | 16653 | 59 | 17030 | 7 | 17485 | 2 |
14781 | 11 | 15158 | 1328 | 15535 | 5401 | 15912 | 3428 | 16289 | 662 | 16666 | 54 | 17043 | 8 | 17498 | 1 |
14794 | 18 | 15171 | 1557 | 15548 | 5568 | 15925 | 3369 | 16302 | 579 | 16679 | 59 | 17056 | 1 | 17511 | 1 |
14807 | 20 | 15184 | 1724 | 15561 | 5671 | 15938 | 3235 | 16315 | 541 | 16692 | 73 | 17069 | 4 | 17524 | 1 |
14820 | 37 | 15197 | 1809 | 15574 | 5617 | 15951 | 3027 | 16328 | 572 | 16705 | 50 | 17082 | 10 | 17537 | 1 |
14833 | 42 | 15210 | 1934 | 15587 | 5752 | 15964 | 2914 | 16341 | 508 | 16718 | 49 | 17095 | 3 | 17550 | 1 |
14846 | 30 | 15223 | 2092 | 15600 | 5577 | 15977 | 2751 | 16354 | 394 | 16731 | 41 | 17108 | 6 | 17563 | 2 |
14859 | 50 | 15236 | 2299 | 15613 | 5632 | 15990 | 2533 | 16367 | 438 | 16744 | 41 | 17121 | 4 | 17654 | 1 |
14872 | 53 | 15249 | 2439 | 15626 | 5669 | 16003 | 2531 | 16380 | 384 | 16757 | 38 | 17134 | 5 | 17693 | 2 |
14885 | 86 | 15262 | 2597 | 15639 | 5764 | 16016 | 2362 | 16393 | 312 | 16770 | 35 | 17147 | 2 | 17823 | 1 |
14898 | 99 | 15275 | 2848 | 15652 | 5552 | 16029 | 2328 | 16406 | 334 | 16783 | 33 | 17173 | 5 | 17888 | 1 |
14911 | 141 | 15288 | 2972 | 15665 | 5459 | 16042 | 2136 | 16419 | 279 | 16796 | 24 | 17186 | 3 | 18070 | 1 |
14924 | 152 | 15301 | 3066 | 15678 | 5353 | 16055 | 2075 | 16432 | 285 | 16809 | 19 | 17199 | 2 | 18083 | 1 |
14937 | 182 | 15314 | 3219 | 15691 | 5379 | 16068 | 1959 | 16445 | 243 | 16822 | 17 | 17212 | 2 | 18473 | 1 |
14950 | 199 | 15327 | 3487 | 15704 | 5482 | 16081 | 1812 | 16458 | 257 | 16835 | 23 | 17225 | 2 | 18655 | 1 |
14963 | 250 | 15340 | 3688 | 15717 | 5213 | 16094 | 1711 | 16471 | 241 | 16848 | 16 | 17251 | 3 | 18967 | 1 |
14976 | 271 | 15353 | 3875 | 15730 | 5359 | 16107 | 1597 | 16484 | 203 | 16861 | 13 | 17264 | 1 | 19071 | 1 |
14989 | 304 | 15366 | 4068 | 15743 | 5048 | 16120 | 1505 | 16497 | 208 | 16874 | 15 | 17277 | 3 |
# | # | # | # | # | # | # | # | ||||||||
14586 | 1 | 15002 | 359 | 15379 | 4280 | 15756 | 4993 | 16133 | 1458 | 16510 | 189 | 16887 | 16 | 17290 | 3 |
14612 | 1 | 15015 | 417 | 15392 | 4282 | 15769 | 4803 | 16146 | 1381 | 16523 | 144 | 16900 | 11 | 17303 | 4 |
14625 | 2 | 15028 | 528 | 15405 | 4380 | 15782 | 4902 | 16159 | 1198 | 16536 | 140 | 16913 | 11 | 17316 | 2 |
14651 | 1 | 15041 | 539 | 15418 | 4551 | 15795 | 4669 | 16172 | 1089 | 16549 | 144 | 16926 | 14 | 17342 | 1 |
14677 | 4 | 15054 | 608 | 15431 | 4766 | 15808 | 4414 | 16185 | 1111 | 16562 | 136 | 16939 | 11 | 17368 | 2 |
14690 | 1 | 15067 | 707 | 15444 | 4805 | 15821 | 4425 | 16198 | 1077 | 16575 | 113 | 16952 | 6 | 17394 | 2 |
14703 | 2 | 15080 | 735 | 15457 | 4842 | 15834 | 4215 | 16211 | 1007 | 16588 | 101 | 16965 | 12 | 17407 | 1 |
14716 | 3 | 15093 | 870 | 15470 | 5185 | 15847 | 4008 | 16224 | 856 | 16601 | 90 | 16978 | 7 | 17420 | 1 |
14729 | 9 | 15106 | 957 | 15483 | 5164 | 15860 | 3988 | 16237 | 876 | 16614 | 88 | 16991 | 7 | 17433 | 1 |
14742 | 4 | 15119 | 1031 | 15496 | 5366 | 15873 | 3865 | 16250 | 767 | 16627 | 70 | 17004 | 4 | 17446 | 3 |
14755 | 6 | 15132 | 1176 | 15509 | 5393 | 15886 | 3854 | 16263 | 762 | 16640 | 83 | 17017 | 3 | 17472 | 2 |
14768 | 8 | 15145 | 1277 | 15522 | 5480 | 15899 | 3611 | 16276 | 706 | 16653 | 59 | 17030 | 7 | 17485 | 2 |
14781 | 11 | 15158 | 1328 | 15535 | 5401 | 15912 | 3428 | 16289 | 662 | 16666 | 54 | 17043 | 8 | 17498 | 1 |
14794 | 18 | 15171 | 1557 | 15548 | 5568 | 15925 | 3369 | 16302 | 579 | 16679 | 59 | 17056 | 1 | 17511 | 1 |
14807 | 20 | 15184 | 1724 | 15561 | 5671 | 15938 | 3235 | 16315 | 541 | 16692 | 73 | 17069 | 4 | 17524 | 1 |
14820 | 37 | 15197 | 1809 | 15574 | 5617 | 15951 | 3027 | 16328 | 572 | 16705 | 50 | 17082 | 10 | 17537 | 1 |
14833 | 42 | 15210 | 1934 | 15587 | 5752 | 15964 | 2914 | 16341 | 508 | 16718 | 49 | 17095 | 3 | 17550 | 1 |
14846 | 30 | 15223 | 2092 | 15600 | 5577 | 15977 | 2751 | 16354 | 394 | 16731 | 41 | 17108 | 6 | 17563 | 2 |
14859 | 50 | 15236 | 2299 | 15613 | 5632 | 15990 | 2533 | 16367 | 438 | 16744 | 41 | 17121 | 4 | 17654 | 1 |
14872 | 53 | 15249 | 2439 | 15626 | 5669 | 16003 | 2531 | 16380 | 384 | 16757 | 38 | 17134 | 5 | 17693 | 2 |
14885 | 86 | 15262 | 2597 | 15639 | 5764 | 16016 | 2362 | 16393 | 312 | 16770 | 35 | 17147 | 2 | 17823 | 1 |
14898 | 99 | 15275 | 2848 | 15652 | 5552 | 16029 | 2328 | 16406 | 334 | 16783 | 33 | 17173 | 5 | 17888 | 1 |
14911 | 141 | 15288 | 2972 | 15665 | 5459 | 16042 | 2136 | 16419 | 279 | 16796 | 24 | 17186 | 3 | 18070 | 1 |
14924 | 152 | 15301 | 3066 | 15678 | 5353 | 16055 | 2075 | 16432 | 285 | 16809 | 19 | 17199 | 2 | 18083 | 1 |
14937 | 182 | 15314 | 3219 | 15691 | 5379 | 16068 | 1959 | 16445 | 243 | 16822 | 17 | 17212 | 2 | 18473 | 1 |
14950 | 199 | 15327 | 3487 | 15704 | 5482 | 16081 | 1812 | 16458 | 257 | 16835 | 23 | 17225 | 2 | 18655 | 1 |
14963 | 250 | 15340 | 3688 | 15717 | 5213 | 16094 | 1711 | 16471 | 241 | 16848 | 16 | 17251 | 3 | 18967 | 1 |
14976 | 271 | 15353 | 3875 | 15730 | 5359 | 16107 | 1597 | 16484 | 203 | 16861 | 13 | 17264 | 1 | 19071 | 1 |
14989 | 304 | 15366 | 4068 | 15743 | 5048 | 16120 | 1505 | 16497 | 208 | 16874 | 15 | 17277 | 3 |
13 | 26 | 39 | 52 | 78 | 156 | 234 | 468 | |
# | 317529 | 4314 | 42 | 167 | 41 | 8 | 1 | 1 |
13 | 26 | 39 | 52 | 78 | 156 | 234 | 468 | |
# | 317529 | 4314 | 42 | 167 | 41 | 8 | 1 | 1 |
13 | 26 | 39 | 78 | 13 | 26 | 39 | 78 | ||
437 | 30 | ||||||||
5 | 7 | 1 | 3 | ||||||
0 | 171 | 18 | 5 | ||||||
13 | 26 | 39 | 78 | 13 | 26 | 39 | 78 | ||
437 | 30 | ||||||||
5 | 7 | 1 | 3 | ||||||
0 | 171 | 18 | 5 | ||||||
13 | 26 | 78 | 246480 | |
# | 172 | 18 | 4 | 1 |
13 | 26 | 78 | 246480 | |
# | 172 | 18 | 4 | 1 |
13 | 26 | 39 | 78 | 13 | 26 | 39 | 13 | 26 | |||
1 | 1 | 6192 | 26 | 7078 | 24 | ||||||
1 | 9815 | 45 | 3632 | 3 | |||||||
5 | 2 | 2 | 14379 | 32 | 1 | 1637 | 14 | ||||
32 | 1 | 18952 | 44 | 604 | 1 | ||||||
121 | 4 | 2 | 22002 | 31 | 1 | 168 | 4 | ||||
294 | 7 | 1 | 22611 | 42 | 50 | ||||||
702 | 11 | 3 | 20758 | 13 | 4 | ||||||
1653 | 12 | 16648 | 38 | ||||||||
3326 | 21 | 2 | 11635 | 8 |
13 | 26 | 39 | 78 | 13 | 26 | 39 | 13 | 26 | |||
1 | 1 | 6192 | 26 | 7078 | 24 | ||||||
1 | 9815 | 45 | 3632 | 3 | |||||||
5 | 2 | 2 | 14379 | 32 | 1 | 1637 | 14 | ||||
32 | 1 | 18952 | 44 | 604 | 1 | ||||||
121 | 4 | 2 | 22002 | 31 | 1 | 168 | 4 | ||||
294 | 7 | 1 | 22611 | 42 | 50 | ||||||
702 | 11 | 3 | 20758 | 13 | 4 | ||||||
1653 | 12 | 16648 | 38 | ||||||||
3326 | 21 | 2 | 11635 | 8 |
13 | 26 | 13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | 39 | ||||
1 | 3199 | 79 | 88751 | 312 | 1 | 3002 | 28 | |||||||
2 | 7856 | 137 | 82010 | 297 | 5 | 1064 | 15 | |||||||
4 | 2 | 16765 | 168 | 1 | 67138 | 223 | 1 | 304 | 2 | |||||
17 | 8 | 30265 | 230 | 46912 | 174 | 2 | 63 | 5 | 1 | |||||
88 | 13 | 48818 | 302 | 28921 | 143 | 2 | 20 | |||||||
411 | 19 | 68292 | 330 | 2 | 15253 | 88 | 1 | 6 | 2 | |||||
1227 | 50 | 83418 | 318 | 3 | 7240 | 51 | 1 | 1 |
13 | 26 | 13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | 39 | ||||
1 | 3199 | 79 | 88751 | 312 | 1 | 3002 | 28 | |||||||
2 | 7856 | 137 | 82010 | 297 | 5 | 1064 | 15 | |||||||
4 | 2 | 16765 | 168 | 1 | 67138 | 223 | 1 | 304 | 2 | |||||
17 | 8 | 30265 | 230 | 46912 | 174 | 2 | 63 | 5 | 1 | |||||
88 | 13 | 48818 | 302 | 28921 | 143 | 2 | 20 | |||||||
411 | 19 | 68292 | 330 | 2 | 15253 | 88 | 1 | 6 | 2 | |||||
1227 | 50 | 83418 | 318 | 3 | 7240 | 51 | 1 | 1 |
13 | 13 | 39 | 13 | 39 | 13 | 39 | ||||
-325 | 1 | -377 | 44 | -429 | 148 | -481 | 38 | |||
-338 | 3 | -390 | 71 | -442 | 133 | -494 | 21 | |||
-351 | 4 | -403 | 123 | 1 | -455 | 100 | -507 | 4 | 1 | |
-364 | 26 | -416 | 146 | -468 | 59 | 1 | -520 | 3 |
13 | 13 | 39 | 13 | 39 | 13 | 39 | ||||
-325 | 1 | -377 | 44 | -429 | 148 | -481 | 38 | |||
-338 | 3 | -390 | 71 | -442 | 133 | -494 | 21 | |||
-351 | 4 | -403 | 123 | 1 | -455 | 100 | -507 | 4 | 1 | |
-364 | 26 | -416 | 146 | -468 | 59 | 1 | -520 | 3 |
13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | 39 | 78 | 13 | 26 | 39 | ||||
4 | 3291 | 41 | 23481 | 92 | 26 | 1 | ||||||||||
14 | 6480 | 67 | 20367 | 89 | 447 | 14 | 1 | |||||||||
47 | 3 | 11032 | 65 | 2 | 15274 | 76 | 156 | 3 | ||||||||
196 | 13 | 16352 | 87 | 9827 | 52 | 36 | ||||||||||
557 | 15 | 20791 | 93 | 5746 | 50 | 1 | 9 | 1 | ||||||||
1446 | 34 | 1 | 23588 | 117 | 2 | 2837 | 19 | 2 | 1 |
13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | 39 | 78 | 13 | 26 | 39 | ||||
4 | 3291 | 41 | 23481 | 92 | 26 | 1 | ||||||||||
14 | 6480 | 67 | 20367 | 89 | 447 | 14 | 1 | |||||||||
47 | 3 | 11032 | 65 | 2 | 15274 | 76 | 156 | 3 | ||||||||
196 | 13 | 16352 | 87 | 9827 | 52 | 36 | ||||||||||
557 | 15 | 20791 | 93 | 5746 | 50 | 1 | 9 | 1 | ||||||||
1446 | 34 | 1 | 23588 | 117 | 2 | 2837 | 19 | 2 | 1 |
13 | 39 | 13 | 26 | 13 | 26 | 39 | |||
1 | 27 | 12 | 5 | ||||||
5 | 1 | 20 | 4 | ||||||
6 | 1218 | 23 | 1 | ||||||
7 | 20 | 2 | 1 | ||||||
20 | 2 | 17 |
13 | 39 | 13 | 26 | 13 | 26 | 39 | |||
1 | 27 | 12 | 5 | ||||||
5 | 1 | 20 | 4 | ||||||
6 | 1218 | 23 | 1 | ||||||
7 | 20 | 2 | 1 | ||||||
20 | 2 | 17 |
13 | 26 | 39 | 78 | 13 | 26 | 39 | 78 | 13 | 26 | 39 | |||
3038 | 2 | 3272 | 36692 | 171 | 3506 | 12054 | 126 | ||||||
3064 | 3 | 3298 | 56508 | 214 | 4 | 3532 | 5477 | 84 | 5 | ||||
3090 | 32 | 1 | 3324 | 75114 | 280 | 3558 | 2154 | 51 | |||||
3116 | 126 | 8 | 3350 | 87114 | 288 | 3584 | 742 | 46 | |||||
3142 | 568 | 16 | 2 | 3376 | 87901 | 334 | 6 | 3610 | 202 | 12 | 1 | ||
3168 | 1602 | 31 | 1 | 3402 | 77847 | 314 | 3636 | 44 | 6 | ||||
3194 | 4452 | 48 | 3428 | 59855 | 288 | 3662 | 13 | 4 | |||||
3220 | 10558 | 70 | 3 | 3454 | 40586 | 214 | 5 | 3688 | 1 | 1 | |||
3246 | 21074 | 145 | 1 | 3480 | 24064 | 207 | 1 |
13 | 26 | 39 | 78 | 13 | 26 | 39 | 78 | 13 | 26 | 39 | |||
3038 | 2 | 3272 | 36692 | 171 | 3506 | 12054 | 126 | ||||||
3064 | 3 | 3298 | 56508 | 214 | 4 | 3532 | 5477 | 84 | 5 | ||||
3090 | 32 | 1 | 3324 | 75114 | 280 | 3558 | 2154 | 51 | |||||
3116 | 126 | 8 | 3350 | 87114 | 288 | 3584 | 742 | 46 | |||||
3142 | 568 | 16 | 2 | 3376 | 87901 | 334 | 6 | 3610 | 202 | 12 | 1 | ||
3168 | 1602 | 31 | 1 | 3402 | 77847 | 314 | 3636 | 44 | 6 | ||||
3194 | 4452 | 48 | 3428 | 59855 | 288 | 3662 | 13 | 4 | |||||
3220 | 10558 | 70 | 3 | 3454 | 40586 | 214 | 5 | 3688 | 1 | 1 | |||
3246 | 21074 | 145 | 1 | 3480 | 24064 | 207 | 1 |
13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | ||||
3040 | 1 | 3222 | 7240 | 51 | 1 | 3404 | 83418 | 318 | 3 | 3586 | 1227 | 50 | ||
3066 | 6 | 2 | 3248 | 15253 | 88 | 1 | 3430 | 68292 | 330 | 2 | 3612 | 411 | 19 | |
3092 | 20 | 3274 | 28921 | 143 | 2 | 3456 | 48818 | 302 | 3638 | 88 | 13 | |||
3118 | 63 | 5 | 1 | 3300 | 46912 | 174 | 2 | 3482 | 30265 | 230 | 3664 | 17 | 8 | |
3144 | 304 | 2 | 3326 | 67138 | 223 | 1 | 3508 | 16765 | 168 | 1 | 3690 | 4 | 2 | |
3170 | 1064 | 15 | 3352 | 82010 | 297 | 5 | 3534 | 7856 | 137 | 3716 | 2 | |||
3196 | 3002 | 28 | 3378 | 88751 | 312 | 1 | 3560 | 3199 | 79 | 3742 | 1 |
13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | 39 | 13 | 26 | ||||
3040 | 1 | 3222 | 7240 | 51 | 1 | 3404 | 83418 | 318 | 3 | 3586 | 1227 | 50 | ||
3066 | 6 | 2 | 3248 | 15253 | 88 | 1 | 3430 | 68292 | 330 | 2 | 3612 | 411 | 19 | |
3092 | 20 | 3274 | 28921 | 143 | 2 | 3456 | 48818 | 302 | 3638 | 88 | 13 | |||
3118 | 63 | 5 | 1 | 3300 | 46912 | 174 | 2 | 3482 | 30265 | 230 | 3664 | 17 | 8 | |
3144 | 304 | 2 | 3326 | 67138 | 223 | 1 | 3508 | 16765 | 168 | 1 | 3690 | 4 | 2 | |
3170 | 1064 | 15 | 3352 | 82010 | 297 | 5 | 3534 | 7856 | 137 | 3716 | 2 | |||
3196 | 3002 | 28 | 3378 | 88751 | 312 | 1 | 3560 | 3199 | 79 | 3742 | 1 |
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