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A134975 Weight distribution of [127,64,19] binary quadratic-residue (or QR) code. 0

%I #7 Nov 11 2017 18:19:06

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8890,48006,0,0,2416302,

%T 10470642,0,0,642229602,2293677150,0,0,80124107595,240372322785,0,0,

%U 5082581311830,12988818908010,0,0,172664602751130,379862126052486,0

%N Weight distribution of [127,64,19] binary quadratic-residue (or QR) code.

%C Taken from the Tjhai-Tomlinson web site.

%C According to Boston and Hao, the Tjhai-Tomlinson tables give several erroneous values. - _Eric M. Schmidt_, Nov 11 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]

%e The weight distribution is:

%e i A_i

%e 0 1

%e 19 8890

%e 20 48006

%e 23 2416302

%e 24 10470642

%e 27 642229602

%e 28 2293677150

%e 31 80124107595

%e 32 240372322785

%e 35 5082581311830

%e 36 12988818908010

%e 39 172664602751130

%e 40 379862126052486

%e 43 3262567479655902

%e 44 6228537915706722

%e 47 35293536896047416

%e 48 58822561493412360

%e 51 223367511592873284

%e 52 326460209251122492

%e 55 840260234424082220

%e 56 1080334587116677140

%e 59 1899366974583683220

%e 60 2152615904528174316

%e 63 2596788489999036307

%e 64 2596788489999036307

%e 67 2152615904528174316

%e 68 1899366974583683220

%e 71 1080334587116677140

%e 72 840260234424082220

%e 75 326460209251122492

%e 76 223367511592873284

%e 79 58822561493412360

%e 80 35293536896047416

%e 83 6228537915706722

%e 84 3262567479655902

%e 87 379862126052486

%e 88 172664602751130

%e 91 12988818908010

%e 92 5082581311830

%e 95 240372322785

%e 96 80124107595

%e 99 2293677150

%e 100 642229602

%e 103 10470642

%e 104 2416302

%e 107 48006

%e 108 8890

%e 127 1

%K nonn,fini

%O 0,20

%A _N. J. A. Sloane_, Apr 11 2009

%E In accordance with Boston and Hao, corrected by _Eric M. Schmidt_, Nov 11 2017

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Last modified May 19 10:22 EDT 2024. Contains 372683 sequences. (Running on oeis4.)