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A105685 Number of inequivalent codes attaining highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n. 3
1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 3, 13, 3 (list; graph; refs; listen; history; text; internal format)



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.


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).


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


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




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



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Last modified September 16 18:24 EDT 2019. Contains 327116 sequences. (Running on oeis4.)