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Self-dual $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes with an automorphism of prime order
1. | Department of Mathematics and Statistics, Loyola University, Chicago, IL 60660, United States |
References:
[1] |
I. M. Araújo, et al., GAP reference manual,, The GAP Group, ().
|
[2] |
J. Bierbrauer, Cyclic additive and quantum stabilizer codes, in "Arithmetic of Finite Fields: First International Workshop'' (eds. C. Carlet and B. Sunar), Madrid, (2007), 276-283. |
[3] |
J. Bierbrauer and Y. Edel, Quantum twisted codes, J. Combin. Des., 8 (2000), 174-188. |
[4] |
S. Bouyuklieva and M. Harada, Extremal self-dual $[50,25,10]$ codes with automorphisms of order 3 and quasi-symmetric 2-$(49,9,6)$ designs, Des. Codes Crypt., 28 (2003), 163-169.
doi: 10.1023/A:1022588407585. |
[5] |
S. Bouyuklieva, A. Malevich and W. Willems, Automorphisms of extremal self-dual codes, IEEE Trans. Inform. Theory, IT-56 (2010), 2091-2096. |
[6] |
S. Bouyuklieva, N. Yankov and R. Russeva, Classification of the binary self-dual $[42,21,8]$ codes having an automorphism of order 3, Finite Fields Appl., 13 (2007), 605-615.
doi: 10.1016/j.ffa.2006.01.001. |
[7] |
S. Bouyuklieva, N. Yankov and R. Russeva, On the classication of binary self-dual $[44,22,8]$ codes with an automorphism of order 3 or 7, Int. J. Inform. Coding Theory, 2 (2011), 21-37. |
[8] |
S. Buyuklieva and V. Yorgov, Singly-even self-dual codes of length 40, Des. Codes Crypt., 9 (1996), 131-141. |
[9] |
A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory, IT-44 (1998), 1369-1387. |
[10] |
L. E. Danielsen, Graph-based classification of self-dual additive codes over finite fields, Adv. Math. Commun., 3 (2009), 329-348. |
[11] |
L. E. Danielsen, On the classification of Hermitian self-dual additive codes over GF(9), IEEE Trans. Inform. Theory, IT-58 (2012), 5500-5511. |
[12] |
B. K. Dey and B. S. Rajan, $\mathbb F_q$-linear cyclic codes over $\mathbb F_{q^m}$: DFT approach, Des. Codes Crypt., 34 (2005), 89-116. |
[13] |
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. |
[14] |
R. Dontcheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 75-79.
doi: 10.1007/s00200-003-0126-4. |
[15] |
W. C. Huffman, Automorphisms of codes with applications to extremal doubly even codes of length 48, IEEE Trans. Inform. Theory, IT-28 (1982), 511-521. |
[16] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 I, IEEE Trans. Inform. Theory, IT-36 (1990), 651-660. |
[17] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 II, IEEE Trans. Inform. Theory, IT-37 (1991), 1206-1216. |
[18] |
W. C. Huffman, On extremal self-dual ternary codes of lengths 28 to 40, IEEE Trans. Inform. Theory, IT-38 (1992), 1395-1400. |
[19] |
W. C. Huffman, Decompositions and extremal type II codes over $\mathbb Z_4$, IEEE Trans. Inform. Theory, IT-44 (1998), 800-809. |
[20] |
W. C. Huffman, Additive self-dual codes over $\mathbb F_4$ with an automorphism of odd prime order, Adv. Math. Commun., 1 (2007), 357-398. |
[21] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$, Adv. Math. Commun., 1 (2007), 429-461. |
[22] |
W. C. Huffman, On the decomposition of self-dual codes over $\mathbb F_2 + u\mathbb F_2$ with an automorphism of odd prime order, Finite Fields Appl., 13 (2007), 681-712.
doi: 10.1016/j.ffa.2006.02.003. |
[23] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$ of even length, Adv. Math. Commun., 2 (2008), 309-343. |
[24] |
W. C. Huffman, Cyclic $\mathbb F_q$-linear $\mathbb F_{q^t}$-codes, Int. J. Inform. Coding Theory, 1 (2010), 249-284. |
[25] |
W. C. Huffman and V. D. Tonchev, The existence of extremal self-dual $[50,25,10]$ codes and quasi-symmetric 2-$(49,9,6)$ designs, Des. Codes Crypt., 6 (1995), 97-106.
doi: 10.1007/BF01398008. |
[26] |
W. C. Huffman and V. D. Tonchev, The $[52,26,10]$ binary self-dual codes with an automorphism of order 7, Finite Fields Appl., 7 (2001), 341-349.
doi: 10.1006/ffta.2000.0295. |
[27] |
V. I. Iorgov, Binary self-dual codes with automorphisms of odd order, Problems Inform. Trans., 19 (1983), 260-270. |
[28] |
V. I. Iorgov, Doubly even extremal codes of length 64, Problems Inform. Trans., 22 (1986), 277-284. |
[29] |
J.-L. Kim and J. Walker, Nonbinary quantum error-correcting codes from algebraic curves, Discrete Math., 308 (2008), 3115-3124. |
[30] |
E. M. Rains, Nonbinary quantum codes, IEEE Trans. Inform. Theory, IT-45 (1999), 1827-1832. |
[31] |
R. P. Russeva, Self-dual $[24,12,8]$ quaternary codes with a nontrivial automorphism of order 3, Finite Fields Appl., 8 (2002), 34-51.
doi: 10.1006/ffta.2001.0322. |
[32] |
N. Yankov and R. Russeva, Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13, IEEE Trans. Inform. Theory, IT-57 (2011), 7498-7506. |
[33] |
V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inform. Theory, IT-33 (1987), 77-82. |
[34] |
V. Y. Yorgov, The extremal codes of length 42 with an automorphism of order 7, Discrete Math., 190 (1998), 201-213. |
[35] |
V. Y. Yorgov and N. Ziapov, Doubly even self-dual $[40,20,8]$ codes with automorphism of an odd order, Problems Inform. Trans., 32 (1996), 253-257. |
show all references
References:
[1] |
I. M. Araújo, et al., GAP reference manual,, The GAP Group, ().
|
[2] |
J. Bierbrauer, Cyclic additive and quantum stabilizer codes, in "Arithmetic of Finite Fields: First International Workshop'' (eds. C. Carlet and B. Sunar), Madrid, (2007), 276-283. |
[3] |
J. Bierbrauer and Y. Edel, Quantum twisted codes, J. Combin. Des., 8 (2000), 174-188. |
[4] |
S. Bouyuklieva and M. Harada, Extremal self-dual $[50,25,10]$ codes with automorphisms of order 3 and quasi-symmetric 2-$(49,9,6)$ designs, Des. Codes Crypt., 28 (2003), 163-169.
doi: 10.1023/A:1022588407585. |
[5] |
S. Bouyuklieva, A. Malevich and W. Willems, Automorphisms of extremal self-dual codes, IEEE Trans. Inform. Theory, IT-56 (2010), 2091-2096. |
[6] |
S. Bouyuklieva, N. Yankov and R. Russeva, Classification of the binary self-dual $[42,21,8]$ codes having an automorphism of order 3, Finite Fields Appl., 13 (2007), 605-615.
doi: 10.1016/j.ffa.2006.01.001. |
[7] |
S. Bouyuklieva, N. Yankov and R. Russeva, On the classication of binary self-dual $[44,22,8]$ codes with an automorphism of order 3 or 7, Int. J. Inform. Coding Theory, 2 (2011), 21-37. |
[8] |
S. Buyuklieva and V. Yorgov, Singly-even self-dual codes of length 40, Des. Codes Crypt., 9 (1996), 131-141. |
[9] |
A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory, IT-44 (1998), 1369-1387. |
[10] |
L. E. Danielsen, Graph-based classification of self-dual additive codes over finite fields, Adv. Math. Commun., 3 (2009), 329-348. |
[11] |
L. E. Danielsen, On the classification of Hermitian self-dual additive codes over GF(9), IEEE Trans. Inform. Theory, IT-58 (2012), 5500-5511. |
[12] |
B. K. Dey and B. S. Rajan, $\mathbb F_q$-linear cyclic codes over $\mathbb F_{q^m}$: DFT approach, Des. Codes Crypt., 34 (2005), 89-116. |
[13] |
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. |
[14] |
R. Dontcheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 75-79.
doi: 10.1007/s00200-003-0126-4. |
[15] |
W. C. Huffman, Automorphisms of codes with applications to extremal doubly even codes of length 48, IEEE Trans. Inform. Theory, IT-28 (1982), 511-521. |
[16] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 I, IEEE Trans. Inform. Theory, IT-36 (1990), 651-660. |
[17] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 II, IEEE Trans. Inform. Theory, IT-37 (1991), 1206-1216. |
[18] |
W. C. Huffman, On extremal self-dual ternary codes of lengths 28 to 40, IEEE Trans. Inform. Theory, IT-38 (1992), 1395-1400. |
[19] |
W. C. Huffman, Decompositions and extremal type II codes over $\mathbb Z_4$, IEEE Trans. Inform. Theory, IT-44 (1998), 800-809. |
[20] |
W. C. Huffman, Additive self-dual codes over $\mathbb F_4$ with an automorphism of odd prime order, Adv. Math. Commun., 1 (2007), 357-398. |
[21] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$, Adv. Math. Commun., 1 (2007), 429-461. |
[22] |
W. C. Huffman, On the decomposition of self-dual codes over $\mathbb F_2 + u\mathbb F_2$ with an automorphism of odd prime order, Finite Fields Appl., 13 (2007), 681-712.
doi: 10.1016/j.ffa.2006.02.003. |
[23] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$ of even length, Adv. Math. Commun., 2 (2008), 309-343. |
[24] |
W. C. Huffman, Cyclic $\mathbb F_q$-linear $\mathbb F_{q^t}$-codes, Int. J. Inform. Coding Theory, 1 (2010), 249-284. |
[25] |
W. C. Huffman and V. D. Tonchev, The existence of extremal self-dual $[50,25,10]$ codes and quasi-symmetric 2-$(49,9,6)$ designs, Des. Codes Crypt., 6 (1995), 97-106.
doi: 10.1007/BF01398008. |
[26] |
W. C. Huffman and V. D. Tonchev, The $[52,26,10]$ binary self-dual codes with an automorphism of order 7, Finite Fields Appl., 7 (2001), 341-349.
doi: 10.1006/ffta.2000.0295. |
[27] |
V. I. Iorgov, Binary self-dual codes with automorphisms of odd order, Problems Inform. Trans., 19 (1983), 260-270. |
[28] |
V. I. Iorgov, Doubly even extremal codes of length 64, Problems Inform. Trans., 22 (1986), 277-284. |
[29] |
J.-L. Kim and J. Walker, Nonbinary quantum error-correcting codes from algebraic curves, Discrete Math., 308 (2008), 3115-3124. |
[30] |
E. M. Rains, Nonbinary quantum codes, IEEE Trans. Inform. Theory, IT-45 (1999), 1827-1832. |
[31] |
R. P. Russeva, Self-dual $[24,12,8]$ quaternary codes with a nontrivial automorphism of order 3, Finite Fields Appl., 8 (2002), 34-51.
doi: 10.1006/ffta.2001.0322. |
[32] |
N. Yankov and R. Russeva, Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13, IEEE Trans. Inform. Theory, IT-57 (2011), 7498-7506. |
[33] |
V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inform. Theory, IT-33 (1987), 77-82. |
[34] |
V. Y. Yorgov, The extremal codes of length 42 with an automorphism of order 7, Discrete Math., 190 (1998), 201-213. |
[35] |
V. Y. Yorgov and N. Ziapov, Doubly even self-dual $[40,20,8]$ codes with automorphism of an odd order, Problems Inform. Trans., 32 (1996), 253-257. |
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