2012, 6(2): 229-235. doi: 10.3934/amc.2012.6.229

Classification of self-dual codes of length 36

1. 

Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan, and PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan

2. 

Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan

Received  June 2011 Published  April 2012

A complete classification of binary self-dual codes of length $36$ is given.
Citation: Masaaki Harada, Akihiro Munemasa. Classification of self-dual codes of length 36. Advances in Mathematics of Communications, 2012, 6 (2) : 229-235. doi: 10.3934/amc.2012.6.229
References:
[1]

C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows,, J. Combin. Theory Ser. A, 105 (2004), 15. doi: 10.1016/j.jcta.2003.09.003.

[2]

R. T. Bilous, Enumeration of the binary self-dual codes of length $34$,, J. Combin. Math. Combin. Comput., 59 (2006), 173.

[3]

R. T. Bilous and G. H. J. van Rees, An enumeration of self-dual codes of length $32$,, Des. Codes Cryptogr., 26 (2002), 61. doi: 10.1023/A:1016544907275.

[4]

W. Bosma and J. Cannon, "Handbook of Magma Functions,'' Department of Mathematics, University of Sydney,, available online at \url{http://magma.maths.usyd.edu.au/magma/+}, ().

[5]

S. Bouyuklieva and I. Bouyukliev, An algorithm for classification of binary self-dual codes,, IEEE Trans. Inform. Theory, ().

[6]

G. D. Cohen, M. G. Karpovsky, H. F. Mattson, Jr. and J. R. Schatz, Covering radius — Survey and recent results,, IEEE Trans. Inform. Theory, 31 (1985), 328. doi: 10.1109/TIT.1985.1057043.

[7]

M. Harada and A. Munemasa, "Database of Self-Dual Codes,'', available online at \url{http://www.math.is.tohoku.ac.jp/~munemasa/selfdualcodes.htm}, ().

[8]

W. C. Huffman, Characterization of quaternary extremal codes of lengths $18$ and $20$,, IEEE Trans. Inform. Theory, 43 (1997), 1613. doi: 10.1109/18.623160.

[9]

C. A. Melchor and P. Gaborit, On the classification of extremal binary self-dual codes,, IEEE Trans. Inform. Theory, 54 (2008), 4743. doi: 10.1109/TIT.2008.928976.

[10]

E. Rains and N. J. A. Sloane, Self-dual codes,, in, (1998), 177.

[11]

J. G. Thompson, Weighted averages associated to some codes,, Scripta Math., 29 (1973), 449.

show all references

References:
[1]

C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows,, J. Combin. Theory Ser. A, 105 (2004), 15. doi: 10.1016/j.jcta.2003.09.003.

[2]

R. T. Bilous, Enumeration of the binary self-dual codes of length $34$,, J. Combin. Math. Combin. Comput., 59 (2006), 173.

[3]

R. T. Bilous and G. H. J. van Rees, An enumeration of self-dual codes of length $32$,, Des. Codes Cryptogr., 26 (2002), 61. doi: 10.1023/A:1016544907275.

[4]

W. Bosma and J. Cannon, "Handbook of Magma Functions,'' Department of Mathematics, University of Sydney,, available online at \url{http://magma.maths.usyd.edu.au/magma/+}, ().

[5]

S. Bouyuklieva and I. Bouyukliev, An algorithm for classification of binary self-dual codes,, IEEE Trans. Inform. Theory, ().

[6]

G. D. Cohen, M. G. Karpovsky, H. F. Mattson, Jr. and J. R. Schatz, Covering radius — Survey and recent results,, IEEE Trans. Inform. Theory, 31 (1985), 328. doi: 10.1109/TIT.1985.1057043.

[7]

M. Harada and A. Munemasa, "Database of Self-Dual Codes,'', available online at \url{http://www.math.is.tohoku.ac.jp/~munemasa/selfdualcodes.htm}, ().

[8]

W. C. Huffman, Characterization of quaternary extremal codes of lengths $18$ and $20$,, IEEE Trans. Inform. Theory, 43 (1997), 1613. doi: 10.1109/18.623160.

[9]

C. A. Melchor and P. Gaborit, On the classification of extremal binary self-dual codes,, IEEE Trans. Inform. Theory, 54 (2008), 4743. doi: 10.1109/TIT.2008.928976.

[10]

E. Rains and N. J. A. Sloane, Self-dual codes,, in, (1998), 177.

[11]

J. G. Thompson, Weighted averages associated to some codes,, Scripta Math., 29 (1973), 449.

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