A110845 - OEIS

%I #15 Mar 10 2020 12:45:31

%S 1,0,0,0,94488,0,74078592,3128434688,312335197020,18125860315136,

%T 552366841342848,9491208609103872,94117043084875944,

%U 549823502398291968,1920604779257215744,4051966906789380096,5193595576952890822,4051966906789380096,1920604779257215744,549823502398291968,94117043084875944,9491208609103872,552366841342848,18125860315136,312335197020,3128434688,74078592,0,94488,0,0,0,1

%N Weight enumerator of [128,64,16] Reed-Muller code RM(3,7).

%D M. Sugino, Y. Ienaga, M. Tokura and T. Kasami, Weight distribution of (128,64) Reed-Muller code, IEEE Trans. Inform. Theory, 17 (1971), 627-628.

%H Masaaki Harada, E Novak, VD Tonchev, <a href="http://arxiv.org/abs/1602.04661">The weight distribution of the self-dual [128, 64] polarity design code</a>, arXiv preprint arXiv:1602.04661, 2016

%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

%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 +94488*x^112 +74078592*x^104 +3128434688*x^100 +312335197020*x^96 +18125860315136*x^92 +552366841342848*x^88+ 9491208609103872*x^84 +94117043084875944*x^80 +549823502398291968*x^76 +1920604779257215744*x^72 +4051966906789380096*x^68 +5193595576952890822*x^64 +4051966906789380096*x^60 +1920604779257215744*x^56 +549823502398291968*x^52 +94117043084875944*x^48 +9491208609103872*x^44 +552366841342848*x^40 +18125860315136*x^36 +312335197020*x^32 +3128434688*x^28 +74078592*x^24 +94488*x^16+1.

%e i A_i

%e 0 1

%e 16 94488

%e 24 74078592

%e 28 3128434688

%e 32 312335197020

%e 36 18125860315136

%e 40 552366841342848

%e 44 9491208609103872

%e 48 94117043084875944

%e 52 549823502398291968

%e 56 1920604779257215744

%e 60 4051966906789380096

%e 64 5193595576952890822

%e 68 4051966906789380096

%e 72 1920604779257215744

%e 76 549823502398291968

%e 80 94117043084875944

%e 84 9491208609103872

%e 88 552366841342848

%e 92 18125860315136

%e 96 312335197020

%e 100 3128434688

%e 104 74078592

%e 112 94488

%e 128 1

%Y Cf. A006006, A006028, A010083, A110846.

%K nonn,fini,full

%O 0,5

%A _N. J. A. Sloane_ and _Nadia Heninger_ Aug 18 2005