A018236 - OEIS

%I #8 Oct 04 2012 10:28:27

%S 1,0,0,0,249849,18106704,462962955,4397342400,16602715899,25756721120,

%T 16602715899,4397342400,462962955,18106704,249849,0,0,0,1

%N Weight distribution of hypothetical [ 72,36,16 ] doubly-even binary self-dual code.

%D N. J. A. Sloane, Is There a (72,36) d = 16 Self-Dual Code?, IEEE Trans. Information Theory, vol. IT-19 (1973), p. 251.

%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>).

%F Let f = x^8 + 14 x^4 y^4 + y^8, g = x^4 y^4 (x^4-y^4)^4. Form the unique linear combination of f^9, f^6 g, f^3 g^2 and g^3 that begins x^72 + A_4 x^68 y^4 + A_8 x^64 y^8 + ..., with A_4 = A_8 = A_12 = 0, Set x=1, replace y^4 by y, and we have the g.f. for this sequence.

%Y Cf. A004675, A019590, A120373.

%K nonn,fini,full

%O 0,5

%A _N. J. A. Sloane_.