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

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8890, 48006, 0, 0, 2416302, 10470642, 0, 0, 642229602, 2293677150, 0, 0, 80124107595, 240372322785, 0, 0, 5082581311830, 12988818908010, 0, 0, 172664602751130, 379862126052486, 0

Offset

0,20

Comments

Taken from the Tjhai-Tomlinson web site.

According to Boston and Hao, the Tjhai-Tomlinson tables give several erroneous values. - Eric M. Schmidt, Nov 11 2017

Links

Table of n, a(n) for n=0..41.

Nigel Boston and Jing Hao, The Weight Distribution of Quasi-quadratic Residue Codes, arXiv:1705.06413 [cs.IT], 2017.

C. J. Tjhai and Martin Tomlinson, Weight Distributions of Quadratic Residue and Quadratic Double Circulant Codes over GF(2) [dead link]

Example

The weight distribution is:
i A_i
0 1
19 8890
20 48006
23 2416302
24 10470642
27 642229602
28 2293677150
31 80124107595
32 240372322785
35 5082581311830
36 12988818908010
39 172664602751130
40 379862126052486
43 3262567479655902
44 6228537915706722
47 35293536896047416
48 58822561493412360
51 223367511592873284
52 326460209251122492
55 840260234424082220
56 1080334587116677140
59 1899366974583683220
60 2152615904528174316
63 2596788489999036307
64 2596788489999036307
67 2152615904528174316
68 1899366974583683220
71 1080334587116677140
72 840260234424082220
75 326460209251122492
76 223367511592873284
79 58822561493412360
80 35293536896047416
83 6228537915706722
84 3262567479655902
87 379862126052486
88 172664602751130
91 12988818908010
92 5082581311830
95 240372322785
96 80124107595
99 2293677150
100 642229602
103 10470642
104 2416302
107 48006
108 8890
127 1

Crossrefs

Sequence in context: A282059 A167290 A043524 * A253664 A037192 A236890

Adjacent sequences: A134972 A134973 A134974 * A134976 A134977 A134978

Keyword

nonn,fini

Author

N. J. A. Sloane, Apr 11 2009

Extensions

In accordance with Boston and Hao, corrected by Eric M. Schmidt, Nov 11 2017

Status

approved