The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080953 Weight distribution of [151,76,19] binary quadratic-residue (or QR) code. 1

%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 7 20:29 EDT 2024. Contains 373206 sequences. (Running on oeis4.)