A110845 Weight enumerator of [128,64,16] Reed-Muller code RM(3,7).

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

Table of n, a(n) for n=0..32.

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

Cf. A006006, A006028, A010083, A110846.

Sequence in context: A031675 A254977 A238143 * A348021 A248067 A252323

Adjacent sequences: A110842 A110843 A110844 * A110846 A110847 A110848

Keyword

nonn,fini,full

Author

N. J. A. Sloane and Nadia Heninger Aug 18 2005

Status

approved