A080953 Weight distribution of [151,76,19] 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, 3775, 24915, 0, 0, 113250, 604000, 0, 0, 30256625, 133993625, 0, 0, 8292705580, 31097645925, 0, 0, 1302257122605, 4196161839505, 0, 0, 113402818847850, 317527892773980, 0

Offset

0,20

Comments

Taken from the Tjhai-Tomlinson web site.

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

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]

M. Tomlinson, C. J. Tjhai, M. A. Ambroze, M. Ahmed, M. Jibril, Error-Correction Coding and Decoding, Springer, 2017, p. 285.

Example

The weight distribution is:
i A_i
0 1
19 3775
20 24915
23 113250
24 604000
27 30256625
28 133993625
31 8292705580
32 31097645925
35 1302257122605
36 4196161839505
39 113402818847850
40 317527892773980
43 5706949034630250
44 14007965812274250
47 171469716029462700
48 371517718063835850
51 3155019195317144883
52 6067344606379124775
55 36274321608490644595
56 62184551328841105020
59 264765917968736096775
60 405974407552062015055
63 1241968201959417159800
64 1707706277694198594725
67 3778485133479463579225
68 4667540459004043244925
71 7503425412744902320620
72 8337139347494335911800
75 9763682329503348632684
76 9763682329503348632684
79 8337139347494335911800
80 7503425412744902320620
83 4667540459004043244925
84 3778485133479463579225
87 1707706277694198594725
88 1241968201959417159800
91 405974407552062015055
92 264765917968736096775
95 62184551328841105020
96 36274321608490644595
99 6067344606379124775
100 3155019195317144883
103 371517718063835850
104 171469716029462700
107 14007965812274250
108 5706949034630250
111 317527892773980
112 113402818847850
115 4196161839505
116 1302257122605
119 31097645925
120 8292705580
123 133993625
124 30256625
127 604000
128 113250
131 24915
132 3775
151 1

Crossrefs

Sequence in context: A367791 A364141 A364766 * A178193 A243777 A135200

Adjacent sequences: A080950 A080951 A080952 * A080954 A080955 A080956

Keyword

nonn,fini

Author

N. J. A. Sloane, Apr 15 2009

Extensions

Corrected (using the Tomlinson et al. book) by Eric M. Schmidt, Nov 17 2017

Status

approved