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A076710 Weight distribution of [137,69,21] binary quadratic-residue (or QR) code. 0
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51238, 270164, 409904, 1947044, 4057118, 17476816, 99448300, 390689750, 1445284240, 5203023264, 18055712240, 59809546795, 189973513945, 581095454420, 1709208146190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,22

COMMENTS

Taken from the Tjhai-Tomlinson web site.

According to Boston and Hao, the Tjhai-Tomlinson web site gives several erroneous values, but their article with Ambroze and Ahmed has correct values. - Eric M. Schmidt, Nov 17 2017

LINKS

Table of n, a(n) for n=0..35.

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]

C. Tjhai, M. Tomlinson, M. Ambroze, M. Ahmed, On the Weight Distribution of the Extended Quadratic Residue Code of Prime 137, arXiv:0801.3926 [cs.IT], 2008.

EXAMPLE

The weight distribution is:

i A_i

0 1

21 51238

22 270164

23 409904

24 1947044

25 4057118

26 17476816

27 99448300

28 390689750

29 1445284240

30 5203023264

31 18055712240

32 59809546795

33 189973513945

34 581095454420

35 1709208146190

36 4842756414205

37 13221982102853

38 34794689744350

39 88328700833460

40 216405317041977

41 511980845799941

42 1170241933257008

43 2585374360137184

44 5523299769383984

45 11414864729214318

46 22829729458428636

47 44202380361406672

48 82879463177637510

49 150535995889831600

50 264943352766103616

51 451961780387038844

52 747475252178564242

53 1198781830242451728

54 1864771735932702688

55 2814110491202421488

56 4120661790689260036

57 5855675469990794812

58 8076793751711441120

59 10814690610004223000

60 14059097793005489900

61 17746731937729182608

62 21754058504313191584

63 25897686719588958304

64 29944200269524733039

65 33629639551783390742

66 36686879511036426264

67 38877142978140092004

68 40020588359850094710

69 40020588359850094710

70 38877142978140092004

71 36686879511036426264

72 33629639551783390742

73 29944200269524733039

74 25897686719588958304

75 21754058504313191584

76 17746731937729182608

77 14059097793005489900

78 10814690610004223000

79 8076793751711441120

80 5855675469990794812

81 4120661790689260036

82 2814110491202421488

83 1864771735932702688

84 1198781830242451728

85 747475252178564242

86 451961780387038844

87 264943352766103616

88 150535995889831600

89 82879463177637510

90 44202380361406672

91 22829729458428636

92 11414864729214318

93 5523299769383984

94 2585374360137184

95 1170241933257008

96 511980845799941

97 216405317041977

98 88328700833460

99 34794689744350

100 13221982102853

101 4842756414205

102 1709208146190

103 581095454420

104 189973513945

105 59809546795

106 18055712240

107 5203023264

108 1445284240

109 390689750

110 99448300

111 17476816

112 4057118

113 1947044

114 409904

115 270164

116 51238

137 1

CROSSREFS

Sequence in context: A252207 A206236 A233901 * A203405 A152512 A203354

Adjacent sequences:  A076707 A076708 A076709 * A076711 A076712 A076713

KEYWORD

nonn,fini,changed

AUTHOR

N. J. A. Sloane, Apr 14 2009

EXTENSIONS

Corrected (using the Tjhai et al. arXiv article) by Eric M. Schmidt, Nov 17 2017

STATUS

approved

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Last modified November 20 04:05 EST 2017. Contains 294959 sequences.