A010080 Weight distribution of [16,11,4] extended Hamming code of length 16.

1, 0, 140, 448, 870, 448, 140, 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. 129.

Links

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

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.

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.

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

Example

W(x,y) = y^16 + 140*y^12*x^4 + 448*y^10*x^6 + 870*y^8*x^8 + 448*y^6*x^10 + 140*y^4*x^12 + x^16.

Mathematica

m:=15; rt=RecurrenceTable[{n*a[n]==Binomial[m, n-1]-a[n-1]-(m-n+2)*a[n-2],
a[0]==1, a[1]==0}, a, {n, 0, m}]; Join[{1}, Table[rt[[i]]+rt[[i+1]], {i, 2, m, 2}], {1}] (* Georg Fischer, Jul 16 2020 *)

Crossrefs

Cf. A110832.

Sequence in context: A255783 A255776 A242319 * A350210 A250801 A184386

Adjacent sequences: A010077 A010078 A010079 * A010081 A010082 A010083

Keyword

nonn,fini,full

Author

N. J. A. Sloane.

Status

approved