A010083 Weight distribution of [128,120,4] extended Hamming code of length 128. This is also the Reed-Muller code RM(5,7).

1, 0, 85344, 42330624, 11170182384, 1772228014592, 185359804775712, 13586256544975872, 729242357526446712, 29627257927486958592, 934817955092922629344, 23382589365749366429184

Offset

0,3

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.

Links

Georg Fischer, Table of n, a(n) for n = 0..64

M. Terada, J. Asatani and T. Koumoto, Weight Distribution

Example

u^128 + 85344*u^124*v^4 + 42330624*u^122*v^6 + 11170182384*u^120*v^8 + 1772228014592*u^118*v^10
+ 185359804775712*u^116*v^12 + 13586256544975872*u^114*v^14 + 729242357526446712*u^112*v^16
+ 29627257927486958592*u^110*v^18 + 934817955092922629344*u^108*v^20 +
23382589365749366429184*u^106*v^22 + 471464166034059302122704*u^104*v^24 +
7769729456174562056216064*u^102*v^26 + 105877979970476869275385504*u^100*v^28 +
1204818392766796825789470720*u^98*v^30 + 11545366574237052418777217820*u^96*v^32 +
93844690870798540052434360320*u^94*v^34 + 651103402851220082586931517920*u^92*v^36 +
3876982708869397190103809681920*u^90*v^38 + 19906815062848699462140058602480*u^88*v^40 +
88505561045975275152200314606080*u^86*v^42 + 341953304041268345847846829061280*u^84*v^44 +
1151738374770880217441839661716480*u^82*v^46 + 3390889310828097487679807613566280*u^80*v^48
+ 8747110385483091255323050018747392*u^78*v^50 +
19809632343594061105640384790579552*u^76*v^52 +
39453146176969302060067713110615552*u^74*v^54 +
69196719366229927819863672056678992*u^72*v^56 +
106997468058126854441956301420662272*u^70*v^58 +
145988070825071389633119654266397216*u^68*v^60 +
175865058349821585715411392357912576*u^66*v^62 +
187118328452563149209991044344449606*u^64*v^64 +
175865058349821585715411392357912576*u^62*v^66 +
145988070825071389633119654266397216*u^60*v^68 +
106997468058126854441956301420662272*u^58*v^70 +
69196719366229927819863672056678992*u^56*v^72 +
39453146176969302060067713110615552*u^54*v^74 +
19809632343594061105640384790579552*u^52*v^76 + 8747110385483091255323050018747392*u^50*v^78
+ 3390889310828097487679807613566280*u^48*v^80 +
1151738374770880217441839661716480*u^46*v^82 + 341953304041268345847846829061280*u^44*v^84 +
88505561045975275152200314606080*u^42*v^86 + 19906815062848699462140058602480*u^40*v^88 +
3876982708869397190103809681920*u^38*v^90 + 651103402851220082586931517920*u^36*v^92 +
93844690870798540052434360320*u^34*v^94 + 11545366574237052418777217820*u^32*v^96 +
1204818392766796825789470720*u^30*v^98 + 105877979970476869275385504*u^28*v^100 +
7769729456174562056216064*u^26*v^102 + 471464166034059302122704*u^24*v^104 +
23382589365749366429184*u^22*v^106 + 934817955092922629344*u^20*v^108 +
29627257927486958592*u^18*v^110 + 729242357526446712*u^16*v^112 +
13586256544975872*u^14*v^114 + 185359804775712*u^12*v^116 + 1772228014592*u^10*v^118 +
11170182384*u^8*v^120 + 42330624*u^6*v^122 + 85344*u^4*v^124 + v^128

Mathematica

m:=127; 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 *)

Crossrefs

Cf. A010080, A010081, A010082.

Sequence in context: A031671 A371641 A371821 * A235968 A195468 A200657

Adjacent sequences: A010080 A010081 A010082 * A010084 A010085 A010086

Keyword

nonn,fini,full

Author

N. J. A. Sloane.

Status

approved