A010031 Weight distribution of any one of the five doubly-even binary [32,16,8] codes (quadratic residue, Reed-Muller, etc.).

1, 0, 620, 13888, 36518, 13888, 620, 0, 1

Offset

0,3

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 443.

Links

Table of n, a(n) for n=0..8.

E. R. Berlekamp and N. J. A. Sloane, Weight Enumerator for Second-Order Reed-Muller Codes, IEEE Trans. Information Theory, IT-16 (1970), 745-751.

J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53.

J. H. Conway, V. S. Pless, and N. J. A. Sloane, The binary self-dual codes of length up to 32: a revised enumeration, J. Combin. Theory, A 60 (1992), 183-195.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745; arXiv preprint, arXiv:math/0509316 [math.NT], 2005-2006.

M. Terada, J. Asatani and T. Koumoto, Weight Distribution

Example

x^32+620*x^24*y^8+13888*x^20*y^12+36518*x^16*y^16+13888*x^12*y^20+620*x^8*y^24+y^32

Crossrefs

Sequence in context: A182351 A335961 A202239 * A252527 A232422 A335767

Adjacent sequences: A010028 A010029 A010030 * A010032 A010033 A010034

Keyword

nonn,fini,full

Author

N. J. A. Sloane.

Status

approved