A080953 - OEIS

%I #15 Nov 18 2017 18:46:12

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3775,24915,0,0,113250,604000,0,

%T 0,30256625,133993625,0,0,8292705580,31097645925,0,0,1302257122605,

%U 4196161839505,0,0,113402818847850,317527892773980,0

%N Weight distribution of [151,76,19] 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 book with Ambroze, Ahmed, and Jibril gives 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 M. Tomlinson, C. J. Tjhai, M. A. Ambroze, M. Ahmed, M. Jibril, <a href="https://dx.doi.org/10.1007/978-3-319-51103-0">Error-Correction Coding and Decoding</a>, Springer, 2017, p. 285.

%e The weight distribution is:

%e i A_i

%e 0 1

%e 19 3775

%e 20 24915

%e 23 113250

%e 24 604000

%e 27 30256625

%e 28 133993625

%e 31 8292705580

%e 32 31097645925

%e 35 1302257122605

%e 36 4196161839505

%e 39 113402818847850

%e 40 317527892773980

%e 43 5706949034630250

%e 44 14007965812274250

%e 47 171469716029462700

%e 48 371517718063835850

%e 51 3155019195317144883

%e 52 6067344606379124775

%e 55 36274321608490644595

%e 56 62184551328841105020

%e 59 264765917968736096775

%e 60 405974407552062015055

%e 63 1241968201959417159800

%e 64 1707706277694198594725

%e 67 3778485133479463579225

%e 68 4667540459004043244925

%e 71 7503425412744902320620

%e 72 8337139347494335911800

%e 75 9763682329503348632684

%e 76 9763682329503348632684

%e 79 8337139347494335911800

%e 80 7503425412744902320620

%e 83 4667540459004043244925

%e 84 3778485133479463579225

%e 87 1707706277694198594725

%e 88 1241968201959417159800

%e 91 405974407552062015055

%e 92 264765917968736096775

%e 95 62184551328841105020

%e 96 36274321608490644595

%e 99 6067344606379124775

%e 100 3155019195317144883

%e 103 371517718063835850

%e 104 171469716029462700

%e 107 14007965812274250

%e 108 5706949034630250

%e 111 317527892773980

%e 112 113402818847850

%e 115 4196161839505

%e 116 1302257122605

%e 119 31097645925

%e 120 8292705580

%e 123 133993625

%e 124 30256625

%e 127 604000

%e 128 113250

%e 131 24915

%e 132 3775

%e 151 1

%K nonn,fini

%O 0,20

%A _N. J. A. Sloane_, Apr 15 2009

%E Corrected (using the Tomlinson et al. book) by _Eric M. Schmidt_, Nov 17 2017