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A010082 Weight distribution of extended Hamming code of length 64. 1
1, 0, 10416, 1166592, 69194232, 2366570752, 51316746768, 747741998592, 7633243745820, 56276359749120, 306558278858160, 1255428754917120, 3916392495228360, 9399341113166592, 17480786291963792 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=0..14.

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

EXAMPLE

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

CROSSREFS

Sequence in context: A031866 A262800 A157445 * A068759 A183787 A204050

Adjacent sequences:  A010079 A010080 A010081 * A010083 A010084 A010085

KEYWORD

nonn,fini

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 15 13:56 EST 2019. Contains 329149 sequences. (Running on oeis4.)