A034415 Second term in extremal weight enumerator of doubly-even binary self-dual code of length 24n.

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

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 Error-Correcting Codes, Elsevier-North 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 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).

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 A303400 A235094

Adjacent sequences: A034412 A034413 A034414 * A034416 A034417 A034418

Keyword

sign

Author

N. J. A. Sloane.

Status

approved