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A034415
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Second term in extremal weight enumerator of doubly-even binary self-dual code of length 24n.
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4
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1, 2576, 535095, 18106704, 369844880, 6101289120, 90184804281, 1251098739072, 16681003659936, 216644275600560, 2763033644875595, 34784314216176096, 433742858109499536, 5369839142579042560
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OFFSET
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0,2
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COMMENTS
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The terms become negative at n=154 and so certainly by that point the extremal codes do not exist (see references).
Up to n = 250 the terms steadily increase in magnitude, but their sign changes from positive to negative at n = 154.
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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, 1978, see Theorem 13, p. 624.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..250
C. L. Mallows and N. J. A. Sloane, An Upper Bound for Self-Dual Codes, Information and Control, 22 (1973), 188-200.
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).
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
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EXAMPLE
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At length 24, the weight enumerator (of the Golay code) is 1+759*x^8+2576*x^12+..., with leading coefficient 759 and second term 2576.
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MAPLE
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For Maple program see A034414.
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CROSSREFS
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Cf. A034414 (leading coefficient), A001380, A034597, A034598.
Sequence in context: A001294 A109026 A217183 * A201510 A303400 A235094
Adjacent sequences: A034412 A034413 A034414 * A034416 A034417 A034418
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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