A076710 - OEIS

%I #15 Mar 14 2020 09:49:47

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,51238,270164,409904,

%T 1947044,4057118,17476816,99448300,390689750,1445284240,5203023264,

%U 18055712240,59809546795,189973513945,581095454420,1709208146190

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

%C Taken from the Tjhai-Tomlinson web site.

%C 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

%H 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.

%H 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]

%H 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.

%e The weight distribution is:

%e i A_i

%e 0 1

%e 21 51238

%e 22 270164

%e 23 409904

%e 24 1947044

%e 25 4057118

%e 26 17476816

%e 27 99448300

%e 28 390689750

%e 29 1445284240

%e 30 5203023264

%e 31 18055712240

%e 32 59809546795

%e 33 189973513945

%e 34 581095454420

%e 35 1709208146190

%e 36 4842756414205

%e 37 13221982102853

%e 38 34794689744350

%e 39 88328700833460

%e 40 216405317041977

%e 41 511980845799941

%e 42 1170241933257008

%e 43 2585374360137184

%e 44 5523299769383984

%e 45 11414864729214318

%e 46 22829729458428636

%e 47 44202380361406672

%e 48 82879463177637510

%e 49 150535995889831600

%e 50 264943352766103616

%e 51 451961780387038844

%e 52 747475252178564242

%e 53 1198781830242451728

%e 54 1864771735932702688

%e 55 2814110491202421488

%e 56 4120661790689260036

%e 57 5855675469990794812

%e 58 8076793751711441120

%e 59 10814690610004223000

%e 60 14059097793005489900

%e 61 17746731937729182608

%e 62 21754058504313191584

%e 63 25897686719588958304

%e 64 29944200269524733039

%e 65 33629639551783390742

%e 66 36686879511036426264

%e 67 38877142978140092004

%e 68 40020588359850094710

%e 69 40020588359850094710

%e 70 38877142978140092004

%e 71 36686879511036426264

%e 72 33629639551783390742

%e 73 29944200269524733039

%e 74 25897686719588958304

%e 75 21754058504313191584

%e 76 17746731937729182608

%e 77 14059097793005489900

%e 78 10814690610004223000

%e 79 8076793751711441120

%e 80 5855675469990794812

%e 81 4120661790689260036

%e 82 2814110491202421488

%e 83 1864771735932702688

%e 84 1198781830242451728

%e 85 747475252178564242

%e 86 451961780387038844

%e 87 264943352766103616

%e 88 150535995889831600

%e 89 82879463177637510

%e 90 44202380361406672

%e 91 22829729458428636

%e 92 11414864729214318

%e 93 5523299769383984

%e 94 2585374360137184

%e 95 1170241933257008

%e 96 511980845799941

%e 97 216405317041977

%e 98 88328700833460

%e 99 34794689744350

%e 100 13221982102853

%e 101 4842756414205

%e 102 1709208146190

%e 103 581095454420

%e 104 189973513945

%e 105 59809546795

%e 106 18055712240

%e 107 5203023264

%e 108 1445284240

%e 109 390689750

%e 110 99448300

%e 111 17476816

%e 112 4057118

%e 113 1947044

%e 114 409904

%e 115 270164

%e 116 51238

%e 137 1

%Y Cf. A097937.

%K nonn,fini

%O 0,22

%A _N. J. A. Sloane_, Apr 14 2009

%E Corrected (using the Tjhai et al. arXiv article) by _Eric M. Schmidt_, Nov 17 2017