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A106433 Weight distribution of [113,57,15] binary quadratic-residue (or QR) code. 0
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3616, 22148, 0, 0, 79100, 371770, 539462, 2255932, 7723324, 28962465, 106963766, 362031208, 1164652580, 3577147210, 10584922440, 29637782832, 79257402672, 203097094347, 498291292415 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,16

COMMENTS

Taken from the Tjhai-Tomlinson web site.

According to Boston and Hao, the Tjhai-Tomlinson tables give erroneous values for a(56) and a(57). The current version (v1) of their paper, however, contains an erroneous correction. - Eric M. Schmidt, Nov 08 2017

LINKS

Table of n, a(n) for n=0..33.

Nigel Boston and Jing Hao, The Weight Distribution of Quasi-quadratic Residue Codes, arXiv:1705.06413 [cs.IT], 2017.

C. J. Tjhai and Martin Tomlinson, Weight Distributions of Quadratic Residue and Quadratic Double Circulant Codes over GF(2) [dead link]

EXAMPLE

The weight distribution is:

i A_i

0 1

15 3616

16 22148

19 79100

20 371770

21 539462

22 2255932

23 7723324

24 28962465

25 106963766

26 362031208

27 1164652580

28 3577147210

29 10584922440

30 29637782832

31 79257402672

32 203097094347

33 498291292415

34 1172450099800

35 2645916266148

36 5732818576654

37 11930503538968

38 23861007077936

39 45892063616140

40 84900317689859

41 151162931905769

42 259136454695604

43 427856747425184

44 680681189085520

45 1043718121981906

46 1542887658581948

47 2199475409482456

48 3024278688038377

49 4011781195731400

50 5135079930536192

51 6343283392924660

52 7563145583871710

53 8704767791530440

54 9671964212811600

55 10375431209297308

56 10745982323915069

57 10745982323915069

58 10375431209297308

59 9671964212811600

60 8704767791530440

61 7563145583871710

62 6343283392924660

63 5135079930536192

64 4011781195731400

65 3024278688038377

66 2199475409482456

67 1542887658581948

68 1043718121981906

69 680681189085520

70 427856747425184

71 259136454695604

72 151162931905769

73 84900317689859

74 45892063616140

75 23861007077936

76 11930503538968

77 5732818576654

78 2645916266148

79 1172450099800

80 498291292415

81 203097094347

82 79257402672

83 29637782832

84 10584922440

85 3577147210

86 1164652580

87 362031208

88 106963766

89 28962465

90 7723324

91 2255932

92 539462

93 371770

94 79100

97 22148

98 3616

113 1

CROSSREFS

Sequence in context: A045817 A107538 A270260 * A188309 A185495 A029829

Adjacent sequences:  A106430 A106431 A106432 * A106434 A106435 A106436

KEYWORD

nonn,fini,changed

AUTHOR

N. J. A. Sloane, Apr 11 2009

EXTENSIONS

In accordance with Boston and Hao, a(56) and a(57) corrected by Eric M. Schmidt, Nov 08 2017

STATUS

approved

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Last modified November 20 10:41 EST 2017. Contains 294963 sequences.