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A034415 Second term in extremal weight enumerator of doubly-even binary self-dual code of length 24n. 4


%S 1,2576,535095,18106704,369844880,6101289120,90184804281,

%T 1251098739072,16681003659936,216644275600560,2763033644875595,

%U 34784314216176096,433742858109499536,5369839142579042560

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

%C The terms become negative at n=154 and so certainly by that point the extremal codes do not exist (see references).

%C Up to n = 250 the terms steadily increase in magnitude, but their sign changes from positive to negative at n = 154.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, see Theorem 13, p. 624.

%H N. J. A. Sloane, <a href="/A034415/b034415.txt">Table of n, a(n) for n = 0..250</a>

%H C. L. Mallows and N. J. A. Sloane, <a href="http://dx.doi.org/10.1016/S0019-9958(73)90273-8">An Upper Bound for Self-Dual Codes</a>, Information and Control, 22 (1973), 188-200.

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (<a href="http://neilsloane.com/doc/self.txt">Abstract</a>, <a href="http://neilsloane.com/doc/self.pdf">pdf</a>, <a href="http://neilsloane.com/doc/self.ps">ps</a>).

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).

%e 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.

%p For Maple program see A034414.

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

%K sign

%O 0,2

%A _N. J. A. Sloane_.

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)