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%I #20 Apr 12 2023 11:26:08
%S 1,0,0,0,10668,0,5291328,112881664,300503590,112881664,5291328,0,
%T 10668,0,0,0,1
%N Weight distribution of [ 128,29,32 ] 2nd-order Reed-Muller code.
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978.
%H E. R. Berlekamp and N. J. A. Sloane, <a href="http://neilsloane.com/doc/rmb.html">Weight Enumerator for Second-Order Reed-Muller Codes</a>, IEEE Trans. Information Theory, IT-16 (1970), 745-751.
%H Claude Carlet and Patrick Solé, <a href="https://arxiv.org/abs/2301.13497">The weight spectrum of several families of Reed-Muller codes</a>, arXiv:2301.13497 [cs.IT], 2023.
%H S. M. Losanitsch, <a href="/A000602/a000602_1.pdf">Die Isomerie-Arten bei den Homologen der Paraffin-Reihe</a>, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
%H 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 x^128+10668*x^96*y^32+5291328*x^80*y^48+112881664*x^72*y^56+300503590*x^64*y^64+112881664*x^56*y^72+5291328*x^48*y^80+10668*x^32*y^96+y^128
%e The weight distribution is:
%e i A_i
%e 0 1
%e 32 10668
%e 48 5291328
%e 56 112881664
%e 64 300503590
%e 72 112881664
%e 80 5291328
%e 96 10668
%e 128 1
%o (Magma) R := ReedMullerCode(2,7); W<x,y> := WeightEnumerator(R); W;
%K nonn,fini,full
%O 0,5
%A _N. J. A. Sloane_
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