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A010082 Weight distribution of extended Hamming code of length 64. 4

%I

%S 1,0,10416,1166592,69194232,2366570752,51316746768,747741998592,

%T 7633243745820,56276359749120,306558278858160,1255428754917120,

%U 3916392495228360,9399341113166592,17480786291963792

%N Weight distribution of extended Hamming code of length 64.

%C Weight enumerator of [64,57,4] Reed-Muller code RM(4,6).

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

%H Georg Fischer, <a href="/A010082/b010082.txt">Table of n, a(n) for n = 0..32</a>

%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 69194232*x^8*y^56 + 25316999607653376*x^30*y^34 + 747741998592*x^14*y^50 + 9399341113166592*x^26*y^38 + 1255428754917120*x^22*y^42 + 306558278858160*x^20*y^44 + 7633243745820*x^16*y^48 + 56276359749120*x^46*y^18 + 306558278858160*x^44*y^20 + y^64 + 28634752793916486*x^32*y^32 + 17480786291963792*x^36*y^28 + 1255428754917120*x^42*y^22 + 17480786291963792*x^28*y^36 + 56276359749120*x^18*y^46 + 10416*x^60*y^4 + 1166592*x^58*y^6 + 1166592*x^6*y^58 + 10416*x^4*y^60 + 51316746768*x^12*y^52 + 9399341113166592*x^38*y^26 + 25316999607653376*x^34*y^30 + 2366570752*x^10*y^54 + 3916392495228360*x^24*y^40 + 51316746768*x^52*y^12 + 747741998592*x^50*y^14 + 7633243745820*x^48*y^16 + 3916392495228360*x^40*y^24 + x^64 + 2366570752*x^54*y^10 + 69194232*x^56*y^8

%e The weight distribution is:

%e i A_i

%e 0 1

%e 4 10416

%e 6 1166592

%e 8 69194232

%e 10 2366570752

%e 12 51316746768

%e 14 747741998592

%e 16 7633243745820

%e 18 56276359749120

%e 20 306558278858160

%e 22 1255428754917120

%e 24 3916392495228360

%e 26 9399341113166592

%e 28 17480786291963792

%e 30 25316999607653376

%e 32 28634752793916486

%e 34 25316999607653376

%e 36 17480786291963792

%e 38 9399341113166592

%e 40 3916392495228360

%e 42 1255428754917120

%e 44 306558278858160

%e 46 56276359749120

%e 48 7633243745820

%e 50 747741998592

%e 52 51316746768

%e 54 2366570752

%e 56 69194232

%e 58 1166592

%e 60 10416

%e 64 1

%t m:=63; 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 *)

%K nonn,fini,full

%O 0,3

%A _N. J. A. Sloane_.

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Last modified October 18 16:05 EDT 2021. Contains 348068 sequences. (Running on oeis4.)