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A110845
Weight enumerator of [128,64,16] Reed-Muller code RM(3,7).
1
1, 0, 0, 0, 94488, 0, 74078592, 3128434688, 312335197020, 18125860315136, 552366841342848, 9491208609103872, 94117043084875944, 549823502398291968, 1920604779257215744, 4051966906789380096, 5193595576952890822, 4051966906789380096, 1920604779257215744, 549823502398291968, 94117043084875944, 9491208609103872, 552366841342848, 18125860315136, 312335197020, 3128434688, 74078592, 0, 94488, 0, 0, 0, 1
OFFSET
0,5
REFERENCES
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.
LINKS
Masaaki Harada, E Novak, VD Tonchev, The weight distribution of the self-dual [128, 64] polarity design code, arXiv preprint arXiv:1602.04661, 2016
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^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.
i A_i
0 1
16 94488
24 74078592
28 3128434688
32 312335197020
36 18125860315136
40 552366841342848
44 9491208609103872
48 94117043084875944
52 549823502398291968
56 1920604779257215744
60 4051966906789380096
64 5193595576952890822
68 4051966906789380096
72 1920604779257215744
76 549823502398291968
80 94117043084875944
84 9491208609103872
88 552366841342848
92 18125860315136
96 312335197020
100 3128434688
104 74078592
112 94488
128 1
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
STATUS
approved