A010081 Weight distribution of extended Hamming code of length 32 (or 3rd-order Reed-Muller code).

1, 0, 1240, 27776, 330460, 2011776, 7063784, 14721280, 18796230, 14721280, 7063784, 2011776, 330460, 27776, 1240, 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..16.

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

x^32 + 1240*x^28*y^4 + 27776*x^26*y^6 + 330460*x^24*y^8 + 2011776*x^22*y^10 + 7063784*x^20*y^12 + 14721280*x^18*y^14 + 18796230*x^16*y^16 + 14721280*x^14*y^18 + 7063784*x^12*y^20 + 2011776*x^10*y^22 + 330460*x^8*y^24 + 27776*x^6*y^26 + 1240*x^4*y^28 + y^32.

Mathematica

m:=31; 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 *)

Prog

(Magma) C := ReedMullerCode(3, 5); W<x, y> := WeightEnumerator(C);
(SageMath)
C = codes.BinaryReedMullerCode(3, 5)
C.weight_distribution()[::2] # Peter Luschny, Jul 16 2020

Crossrefs

Sequence in context: A145047 A236974 A237552 * A028514 A099178 A209711

Adjacent sequences: A010078 A010079 A010080 * A010082 A010083 A010084

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Status

approved