0,2

The term after the leading nonzero term eventually becomes negative, and so for large n the extremal codes do not exist (see references, also A034415).

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

C. L. Mallows and N. J. A. Sloane, An Upper Bound for Self-Dual Codes, Information and Control, 22 (1973), 188-200.

N. J. A. Sloane, Table of n, a(n) for n = 0..250

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).

a(24n) = C(24n, 5)*C(5n-2, n-1)/C(4n+4, 5).

At length 24, the extremal weight enumerator is 1+759*x^8+2576*x^12+..., with leading coefficient 759; this is the weight enumerator of the binary Golay code.

# Extremal weight enumerators: read(`/usr/njas/bin/format`); kernelopts(printbytes=false): interface(screenwidth=200);

W0:=1; f:=1+14*x+x^2; f:=f^3; g:=x*(1-x)^4;

for mu from 1 to 100 do

# set max deg

md:=mu+3; W0:=series(f^mu, x, md): h:=series(g/f, x, md): A:=series(W0, x, md): Z:=A:

for i from 1 to mu do

Z:=series(Z*h, x, md); A:=series(A-coeff(A, x, i)*Z, x, md); od: lprint(A);

od:

Cf. A034415 (second coefficient, which becmes negative), A001380, A034597.

Sequence in context: A001293 A001380 A001920 this_sequence A014747 A022051 A107515

Adjacent sequences: A034411 A034412 A034413 this_sequence A034415 A034416 A034417

nonn,easy,nice

njas