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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice

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

• 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.

Extensions

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

Name clarified by Nathan J. Russell, Nov 26 2018