

A034415


Second term in extremal weight enumerator of doublyeven binary selfdual code of length 24n.


4



1, 2576, 535095, 18106704, 369844880, 6101289120, 90184804281, 1251098739072, 16681003659936, 216644275600560, 2763033644875595, 34784314216176096, 433742858109499536, 5369839142579042560
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OFFSET

0,2


COMMENTS

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.


REFERENCES

F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, ElsevierNorth Holland, 1978, see Theorem 13, p. 624.


LINKS

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 SelfDual Codes, Information and Control, 22 (1973), 188200.
G. Nebe, E. M. Rains and N. J. A. Sloane, SelfDual Codes and Invariant Theory, Springer, Berlin, 2006.
E. M. Rains and N. J. A. Sloane, Selfdual codes, pp. 177294 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).


EXAMPLE

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.


MAPLE

For Maple program see A034414.


CROSSREFS

Cf. A034414 (leading coefficient), A001380, A034597, A034598.
Sequence in context: A001294 A109026 A217183 * A201510 A235094 A171257
Adjacent sequences: A034412 A034413 A034414 * A034416 A034417 A034418


KEYWORD

sign


AUTHOR

N. J. A. Sloane.


STATUS

approved



