`a`
Advances in Mathematics of Communications (AMC)
 

Construction of self-dual codes with an automorphism of order $p$
Pages: 23 - 36, Volume 5, Issue 1, February 2011

doi:10.3934/amc.2011.5.23      Abstract        References        Full text (353.3K)           Related Articles

Hyun Jin Kim - Department of Mathematics, Yonsei University, 134 Shinchon-dong, Seodaemun-Gu, Seoul 120-749, South Korea (email)
Heisook Lee - Department of Mathematics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul, 120-750, South Korea (email)
June Bok Lee - Department of Mathematics, Yonsei University, 134 Shinchon-dong, Seodaemun-Gu, Seoul 120-749, South Korea (email)
Yoonjin Lee - Department of Mathematics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul, 120-750, South Korea (email)

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.       
2 S. Bouyuklieva, A method for constructing self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 46 (2000), 496-504.       
3 S. Bouyuklieva and I. Bouyukliev, Extremal self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 44 (1998), 323-328.       
4 S. Bouyuklieva and P. Östergård, New constructions of optimal self-dual binary codes of length $54$, Des. Codes Crypt., 41 (2006), 101-109.       
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.       
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.       
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.       
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.       
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.       
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.       
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.       
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.       
15 J.-L. Kim, New extremal self-dual codes of length $36$, $38$, and $58$, IEEE Trans. Inform. Theory, 47 (2001), 386-393.       
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.       
17 V. Pless, A classification of self-orthogonal codes over $GF(2)$, Discrete Math., 3 (1972), 209-246.       
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.       
19 H.-P. Tsai, Existence of certain extremal self-dual codes, IEEE Trans. Inform. Theory, 38 (1992), 501-504.       
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.       
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.       
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.       

Go to top