A003179 Number of self-dual binary codes of length 2n (up to column permutation equivalence). (Formerly M0289)

1, 1, 1, 1, 2, 2, 3, 4, 7, 9, 16, 25, 55, 103, 261, 731, 3295, 24147, 519492

Offset

0,5

Comments

The length 36 binary self dual codes have been classified. - Nathan J. Russell, Feb 14 2016

This is number of binary self-dual codes of length 2n up to column permutation equivalence. Sequence A028362 gives an actual count of all possible binary self-dual codes of length 2n. - Nathan J. Russell, Nov 25 2018

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..18.

R. T. Bilous and G. H. J. van Rees, An enumeration of binary self-dual codes of length 32, preprint.

R. T. Bilous and G. H. J. van Rees, An enumeration of binary self-dual codes of length 32, Designs, Codes Crypt., 26 (2002), 61-86.

J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. MR0558873

J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A28 (1980), 26-53 (Abstract, pdf, ps, Table A, Table D).

Masaaki Harada and Akihiro Munemasa, Classification of Self-Dual Codes of Length 36, arXiv:1012.5464 [math.CO], 2010-2012.

W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic. 11 (2005), 451-490.

W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003, Pages 7,252-282,338-393.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

Crossrefs

Cf. A003178, A028362, A028363, A105685. Equals A106163 + A106165.

Sequence in context: A241415 A323357 A322299 * A153934 A361440 A143590

Adjacent sequences: A003176 A003177 A003178 * A003180 A003181 A003182

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane

Extensions

a(18) from Nathan J. Russell, Feb 14 2016

Name clarified by Nathan J. Russell, Nov 26 2018

Status

approved