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 A010081 Weight distribution of extended Hamming code of length 32 (or 3rd order Reed-Muller code). 3
 1, 0, 1240, 27776, 330460, 2011776, 7063784, 14721280, 18796230, 14721280, 7063784, 2011776, 330460, 27776, 1240, 0, 1 (list; graph; refs; listen; history; text; internal format)
 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 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 := 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 STATUS approved

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Last modified August 2 12:00 EDT 2021. Contains 346422 sequences. (Running on oeis4.)