A018236 Weight distribution of hypothetical [ 72,36,16 ] doubly-even binary self-dual code.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

References

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

Links

• E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

Crossrefs

Cf. A004675, A019590, A120373.

Formula

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.