cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A003178 Number of indecomposable self-dual binary codes of length 2n.

Original entry on oeis.org

1, 1, 0, 0, 1, 0, 1, 1, 2, 2, 6, 8, 26, 45, 148, 457, 2523, 20786
Offset: 0

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Author

N. J. A. Sloane

Keywords

References

  • R. T. Bilous, Enumeration of binary self-dual codes of length 34, Preprint, 2005.
  • 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.
  • V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

  • G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
  • 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).
  • 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. A003179, A028362, A028363. Equals A106162 + A106164.

Extensions

a(16) corrected and a(17) added by N. J. A. Sloane, based on data in Bilous's paper, Sep 06 2005

A106163 Total number of (indecomposable or decomposable) Type II binary self-dual codes of length 8n.

Original entry on oeis.org

1, 1, 2, 9, 85, 94343
Offset: 0

Views

Author

N. J. A. Sloane, May 09 2005

Keywords

Comments

"There are 94343 inequivalent doubly even self-dual codes of length 40, 16470 of which are extremal" [Betsumiya et al.] - Jonathan Vos Post, Aug 06 2012

Links

  • Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, A Complete Classification of Doubly Even Self-Dual Codes of Length 40, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012. - From _Jonathan Vos Post_, Aug 06 2012
  • J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. [DOI] 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, A60 (1992), 183-195 (Abstract, pdf, ps, Table A, Table D).
  • W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic. 11 (2005), 451-490. [DOI]
  • G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
  • V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746. [DOI] MR0514353
  • 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, A003179, A106162, A106163, A106164, A106165, A106166, A106167, A215219.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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