A105685 Number of inequivalent codes attaining highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n.

1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 3, 13, 3

Offset

1,5

References

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

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.

V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.

Links

Table of n, a(n) for n=1..16.

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).

P. Gaborit, Tables of Self-Dual Codes

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).

Example

At length 8 the only strictly Type I self-dual code is {00,11}^4, so a(4) = 1.

Crossrefs

Cf. A105674, A105675, A105676, A105677, A105678, A016729, A066016, A105681, A105682.

A105674 gives the minimal distance of these codes, A106165 the number of codes of any minimal distance and A003179 the number of inequivalent codes allowing Type I or Type II and any minimal distance.

Sequence in context: A165680 A248049 A231867 * A228239 A173749 A323618

Adjacent sequences: A105682 A105683 A105684 * A105686 A105687 A105688

Keyword

nonn

Author

N. J. A. Sloane, May 06 2005, Aug 23 2008

Status

approved