The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A076710 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A076710

Weight distribution of [137, 69, 21] binary quadratic-residue (or QR) code.
(history; published version)

#15 by Peter Luschny at Sat Mar 14 09:49:47 EDT 2020

STATUS

editing

approved

#14 by Peter Luschny at Sat Mar 14 09:46:51 EDT 2020

NAME

Weight distribution of [137, 69, 21] binary quadratic-residue (or QR) code.

Discussion

Sat Mar 14

09:49

Peter Luschny: Thanks Hugo! The changes made by Eric are OK. The correct values are in the arXiv version as Prof. Martin Tomlinson has confirmed in an email.

#13 by Peter Luschny at Fri Mar 13 16:30:05 EDT 2020

STATUS

proposed

editing

#12 by Hugo Pfoertner at Fri Mar 13 13:43:46 EDT 2020

STATUS

editing

proposed

Discussion

Fri Mar 13

16:30

Peter Luschny: I put this in the edit state. As soon as I know more I will come back.

#11 by Hugo Pfoertner at Fri Mar 13 13:35:13 EDT 2020

CROSSREFS

Cf. A097937.

STATUS

approved

editing

Discussion

Fri Mar 13

13:43

Hugo Pfoertner: In view of the current discussion in A097937 and the last change by Neil there, it seems to be doubtful whether the changes made here were actually justified and whether the changed table represents the correct version. Clarification seems to me to be necessary.

#10 by N. J. A. Sloane at Sat Nov 18 18:46:02 EST 2017

STATUS

proposed

approved

#9 by Eric M. Schmidt at Sat Nov 18 15:52:47 EST 2017

STATUS

editing

proposed

#8 by Eric M. Schmidt at Fri Nov 17 23:24:00 EST 2017

EXTENSIONS

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

#7 by Eric M. Schmidt at Fri Nov 17 23:05:11 EST 2017

COMMENTS

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

Nigel Boston and Jing Hao, <a href="https://arxiv.org/abs/1705.06413">The Weight Distribution of Quasi-quadratic Residue Codes</a>, arXiv:1705.06413 [cs.IT], 2017.

C. J. Tjhai and Martin Tomlinson, <a href="http://www.tech.plym.ac.uk/Research/fixed_and_mobile_communications/links/weightdistributions.htm"> Weight Distributions of Quadratic Residue and Quadratic Double Circulant Codes over GF(2)</a> [dead link]

C. Tjhai, M. Tomlinson, M. Ambroze, M. Ahmed, <a href="https://arxiv.org/abs/0801.3926">On the Weight Distribution of the Extended Quadratic Residue Code of Prime 137</a>, arXiv:0801.3926 [cs.IT], 2008.

EXTENSIONS

Corrected from Tjhai et al. arXiv article by Eric M. Schmidt, Nov 17 2017

Discussion

Fri Nov 17

23:08

Eric M. Schmidt: I have sanity checked the new values using the four checks mentioned in Boston and Hao, p. 16.

#6 by Eric M. Schmidt at Sat Nov 11 15:37:03 EST 2017

EXAMPLE

48 8287946317763750482879463177637510

49 150535995889831616150535995889831600

51 451961780387038848451961780387038844

52 747475252178564224747475252178564242

53 11987818302424517121198781830242451728

54 18647717359327027201864771735932702688

55 28141104912024212482814110491202421488

56 41206617906892600324120661790689260036

57 58556754699907952645855675469990794812

58 80767937517114408968076793751711441120

59 1081469061000422400010814690610004223000

60 1405909779300549017614059097793005489900

61 1774673193772918169617746731937729182608

62 2175405850431319244821754058504313191584

63 2589768671958895820825897686719588958304

64 2994420026952473395229944200269524733039

65 3362963955178339123233629639551783390742

66 3668687951103642828836686879511036426264

67 3887714297814009446438877142978140092004

68 4002058835985009868840020588359850094710

69 4002058835985009868840020588359850094710

70 3887714297814009446438877142978140092004

71 3668687951103642828836686879511036426264

72 3362963955178339123233629639551783390742

73 2994420026952473395229944200269524733039

74 2589768671958895820825897686719588958304

75 2175405850431319244821754058504313191584

76 1774673193772918169617746731937729182608

77 1405909779300549017614059097793005489900

78 1081469061000422400010814690610004223000

79 80767937517114408968076793751711441120

80 58556754699907952645855675469990794812

81 41206617906892600324120661790689260036

82 28141104912024212482814110491202421488

83 18647717359327027201864771735932702688

84 11987818302424517121198781830242451728

85 747475252178564224747475252178564242

86 451961780387038848451961780387038844

88 150535995889831616150535995889831600

89 8287946317763750482879463177637510

STATUS

approved

editing