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

Author

N. J. A. Sloane

Keywords

• sign

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.

Examples

			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.
		

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).

Crossrefs

Cf. A034414 (leading coefficient), A001380, A034597, A034598.

Programs

Maple

For Maple program see A034414.