cp's OEIS Frontend

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

%I A010081 #23 Aug 12 2023 23:00:29
%S A010081 1,0,1240,27776,330460,2011776,7063784,14721280,18796230,14721280,
%T A010081 7063784,2011776,330460,27776,1240,0,1
%N A010081 Weight distribution of extended Hamming code of length 32 (or 3rd-order Reed-Muller code).
%D A010081 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.
%H A010081 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H A010081 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%H A010081 M. Terada, J. Asatani and T. Koumoto, <a href="http://isec.ec.okayama-u.ac.jp/home/kusaka/wd/index.html">Weight Distribution</a>
%e A010081 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.
%t A010081 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 *)
%o A010081 (Magma) C := ReedMullerCode(3,5); W<x,y> := WeightEnumerator(C);
%o A010081 (SageMath)
%o A010081 C = codes.BinaryReedMullerCode(3, 5)
%o A010081 C.weight_distribution()[::2] # _Peter Luschny_, Jul 16 2020
%K A010081 nonn,fini,full
%O A010081 0,3
%A A010081 _N. J. A. Sloane_