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Construction of self-dual codes with an automorphism of order $p$
1. | Department of Mathematics, Yonsei University, 134 Shinchon-dong, Seodaemun-Gu, Seoul 120-749, South Korea, South Korea |
2. | Department of Mathematics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul, 120-750, South Korea, South Korea |
References:
[1] |
I. Bouyukliev and S. Bouyuklieva, Some new extremal self-dual codes with lengths $44, 50, 54,$ and $58$, IEEE Trans. Inform. Theory, 44 (1998), 809-812.
doi: 10.1109/18.661526. |
[2] |
S. Bouyuklieva, A method for constructing self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 46 (2000), 496-504.
doi: 10.1109/18.825812. |
[3] |
S. Bouyuklieva and I. Bouyukliev, Extremal self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 44 (1998), 323-328.
doi: 10.1109/18.651059. |
[4] |
S. Bouyuklieva and P. Östergård, New constructions of optimal self-dual binary codes of length $54$, Des. Codes Crypt., 41 (2006), 101-109.
doi: 10.1007/s10623-006-0018-2. |
[5] |
S. Bouyuklieva, R. Russeva and N. Yankov, On the structure of binary self-dual codes having an automorphism of order a square of an odd prime, IEEE Trans. Inform. Theory, 51 (2005), 3678-3686.
doi: 10.1109/TIT.2005.855616. |
[6] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1991), 1319-1333.
doi: 10.1109/18.59931. |
[7] |
R. Dontcheva and M. Harada, Extremal self-dual codes of length 62 and related extremal self-dual codes, IEEE Trans. Inform. Theory, 48 (2002), 2060-2064.
doi: 10.1109/TIT.2002.1013144. |
[8] |
R. Dontcheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7, Algebra Eng. Commun. Comput. (AAECC J.), 14 (2003), 75-79. |
[9] |
S. T. Dougherty, T. A. Gulliver and M. Harada, Extremal binary self-dual codes, IEEE Trans. Inform. Theory, 43 (1997), 2036-2047.
doi: 10.1109/18.641574. |
[10] |
T. A. Gulliver, J.-L. Kim and Y. Lee, New MDS and near-MDS self-dual codes, IEEE Trans. Inform. Theory, 54 (2008), 4354-4360.
doi: 10.1109/TIT.2008.928297. |
[11] |
M. Harada, T. A. Gulliver and H. Kaneta, Classification of extremal double-circulant self-dual codes of length up to 62, Discrete Math., 188 (1998), 127-136.
doi: 10.1016/S0012-365X(97)00250-1. |
[12] |
M. Harada and H. Kimura, On extremal self-dual codes, Math. J. Okayama Univ., 37 (1995), 1-14. |
[13] |
W. C. Huffman, Automorphisms of codes with application to extremal doubly-even codes of length $48$, IEEE Trans. Inform. Theory, 28 (1982), 511-521.
doi: 10.1109/TIT.1982.1056499. |
[14] |
W. C. Huffman, 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. |
[15] |
J.-L. Kim, New extremal self-dual codes of length $36$, $38$, and $58$, IEEE Trans. Inform. Theory, 47 (2001), 386-393.
doi: 10.1109/18.904540. |
[16] |
J.-L. Kim and Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A, 105 (2004), 79-95.
doi: 10.1016/j.jcta.2003.10.003. |
[17] |
V. Pless, A classification of self-orthogonal codes over $GF(2)$, Discrete Math., 3 (1972), 209-246.
doi: 10.1016/0012-365X(72)90034-9. |
[18] |
V. Pless, N. J. A. Sloane and H. N. Ward, Ternary codes of minimum weight 6 and the classification of the self-dual codes of length 20, IEEE Trans. Inform. Theory, 26 (1980), 306-316.
doi: 10.1109/TIT.1980.1056195. |
[19] |
H.-P. Tsai, Existence of certain extremal self-dual codes, IEEE Trans. Inform. Theory, 38 (1992), 501-504.
doi: 10.1109/18.119711. |
[20] |
H.-P. Tsai and Y. J. Jiang, Some new extremal self-dual $[58,29,10]$ codes, IEEE Trans. Inform. Theory, 44 (1998), 813-814.
doi: 10.1109/18.661527. |
[21] |
V. Y. Yorgov, Binary self-dual codes with automorphisms of an odd order, Problems Inform. Trans., 19 (1983), 260-270. |
[22] |
V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inform. Theory, 33 (1987), 77-82.
doi: 10.1109/TIT.1987.1057273. |
[23] |
S. Zhang and S. Li, Some new extremal self-dual codes with lengths $42, 44, 52,$ and $58$, Discrete Math., 238 (2001), 147-150.
doi: 10.1016/S0012-365X(00)00420-9. |
show all references
References:
[1] |
I. Bouyukliev and S. Bouyuklieva, Some new extremal self-dual codes with lengths $44, 50, 54,$ and $58$, IEEE Trans. Inform. Theory, 44 (1998), 809-812.
doi: 10.1109/18.661526. |
[2] |
S. Bouyuklieva, A method for constructing self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 46 (2000), 496-504.
doi: 10.1109/18.825812. |
[3] |
S. Bouyuklieva and I. Bouyukliev, Extremal self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 44 (1998), 323-328.
doi: 10.1109/18.651059. |
[4] |
S. Bouyuklieva and P. Östergård, New constructions of optimal self-dual binary codes of length $54$, Des. Codes Crypt., 41 (2006), 101-109.
doi: 10.1007/s10623-006-0018-2. |
[5] |
S. Bouyuklieva, R. Russeva and N. Yankov, On the structure of binary self-dual codes having an automorphism of order a square of an odd prime, IEEE Trans. Inform. Theory, 51 (2005), 3678-3686.
doi: 10.1109/TIT.2005.855616. |
[6] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1991), 1319-1333.
doi: 10.1109/18.59931. |
[7] |
R. Dontcheva and M. Harada, Extremal self-dual codes of length 62 and related extremal self-dual codes, IEEE Trans. Inform. Theory, 48 (2002), 2060-2064.
doi: 10.1109/TIT.2002.1013144. |
[8] |
R. Dontcheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7, Algebra Eng. Commun. Comput. (AAECC J.), 14 (2003), 75-79. |
[9] |
S. T. Dougherty, T. A. Gulliver and M. Harada, Extremal binary self-dual codes, IEEE Trans. Inform. Theory, 43 (1997), 2036-2047.
doi: 10.1109/18.641574. |
[10] |
T. A. Gulliver, J.-L. Kim and Y. Lee, New MDS and near-MDS self-dual codes, IEEE Trans. Inform. Theory, 54 (2008), 4354-4360.
doi: 10.1109/TIT.2008.928297. |
[11] |
M. Harada, T. A. Gulliver and H. Kaneta, Classification of extremal double-circulant self-dual codes of length up to 62, Discrete Math., 188 (1998), 127-136.
doi: 10.1016/S0012-365X(97)00250-1. |
[12] |
M. Harada and H. Kimura, On extremal self-dual codes, Math. J. Okayama Univ., 37 (1995), 1-14. |
[13] |
W. C. Huffman, Automorphisms of codes with application to extremal doubly-even codes of length $48$, IEEE Trans. Inform. Theory, 28 (1982), 511-521.
doi: 10.1109/TIT.1982.1056499. |
[14] |
W. C. Huffman, 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. |
[15] |
J.-L. Kim, New extremal self-dual codes of length $36$, $38$, and $58$, IEEE Trans. Inform. Theory, 47 (2001), 386-393.
doi: 10.1109/18.904540. |
[16] |
J.-L. Kim and Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A, 105 (2004), 79-95.
doi: 10.1016/j.jcta.2003.10.003. |
[17] |
V. Pless, A classification of self-orthogonal codes over $GF(2)$, Discrete Math., 3 (1972), 209-246.
doi: 10.1016/0012-365X(72)90034-9. |
[18] |
V. Pless, N. J. A. Sloane and H. N. Ward, Ternary codes of minimum weight 6 and the classification of the self-dual codes of length 20, IEEE Trans. Inform. Theory, 26 (1980), 306-316.
doi: 10.1109/TIT.1980.1056195. |
[19] |
H.-P. Tsai, Existence of certain extremal self-dual codes, IEEE Trans. Inform. Theory, 38 (1992), 501-504.
doi: 10.1109/18.119711. |
[20] |
H.-P. Tsai and Y. J. Jiang, Some new extremal self-dual $[58,29,10]$ codes, IEEE Trans. Inform. Theory, 44 (1998), 813-814.
doi: 10.1109/18.661527. |
[21] |
V. Y. Yorgov, Binary self-dual codes with automorphisms of an odd order, Problems Inform. Trans., 19 (1983), 260-270. |
[22] |
V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inform. Theory, 33 (1987), 77-82.
doi: 10.1109/TIT.1987.1057273. |
[23] |
S. Zhang and S. Li, Some new extremal self-dual codes with lengths $42, 44, 52,$ and $58$, Discrete Math., 238 (2001), 147-150.
doi: 10.1016/S0012-365X(00)00420-9. |
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