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Search: id:A105675
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| A105675 |
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Highest minimal distance of any Type II doubly-even binary self-dual code of length 8n. |
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+0
20
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OFFSET
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1,1
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.
N. J. A. Sloane, Is There a (72,36) d = 16 Self-Dual Code?, IEEE Trans. Information Theory, vol. IT-19 (1973), p. 251.
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LINKS
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G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
P. Gaborit, Tables of Self-Dual Codes
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
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At length 8 the only Type II doubly-even self-dual code is the Hamming code e_8, which has d=4, so a(1) = 4. The [24,12,8] Golay code has d=8, so a(3) = 8.
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CROSSREFS
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Cf. A105674, A105676, A105677, A105678, A016729, A066016, A105681, A105682.
Cf. also A001380, A018236.
Sequence in context: A019674 A016712 A076359 this_sequence A053249 A071339 A146890
Adjacent sequences: A105672 A105673 A105674 this_sequence A105676 A105677 A105678
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 06 2005
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EXTENSIONS
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Is a(9) = 12 or 16? This is an open question of long standing.
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