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A105685
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Number of inequivalent codes attaining highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n.
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3
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1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 3, 13, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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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.
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LINKS
| 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).
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EXAMPLE
| At length 8 the only strictly Type I self-dual code is {00,11}^4, so a(4) = 1.
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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: A126886 A179272 A165680 * A173749 A125090 A073266
Adjacent sequences: A105682 A105683 A105684 * A105686 A105687 A105688
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 06 2005, Aug 23 2008
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