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A010082
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Weight distribution of extended Hamming code of length 64.
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4
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1, 0, 10416, 1166592, 69194232, 2366570752, 51316746768, 747741998592, 7633243745820, 56276359749120, 306558278858160, 1255428754917120, 3916392495228360, 9399341113166592, 17480786291963792
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OFFSET
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0,3
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COMMENTS
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Weight enumerator of [64,57,4] Reed-Muller code RM(4,6).
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 129.
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LINKS
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EXAMPLE
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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
The weight distribution is:
i A_i
0 1
4 10416
6 1166592
8 69194232
10 2366570752
12 51316746768
14 747741998592
16 7633243745820
18 56276359749120
20 306558278858160
22 1255428754917120
24 3916392495228360
26 9399341113166592
28 17480786291963792
30 25316999607653376
32 28634752793916486
34 25316999607653376
36 17480786291963792
38 9399341113166592
40 3916392495228360
42 1255428754917120
44 306558278858160
46 56276359749120
48 7633243745820
50 747741998592
52 51316746768
54 2366570752
56 69194232
58 1166592
60 10416
64 1
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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