A146888 Weight distribution of [167,84,23] 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, 0, 0, 0, 0, 110888, 665328, 0, 0, 3021698, 15108490, 0, 0, 1057206192, 4493126316, 0, 0, 268132007628, 983150694636, 0, 0, 39540857275985, 126530743283152, 0, 0

Offset

0,24

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..42.

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. 286.

Example

The weight distribution is:
i A_i
0 1
23 110888
24 665328
27 3021698
28 15108490
31 1057206192
32 4493126316
35 268132007628
36 983150694636
39 39540857275985
40 126530743283152
43 3417107288264670
44 9630029630564070
47 179728155397349776
48 449320388493374440
51 5907921405841809432
52 13179209289954805656
55 124033230083117023704
56 248066460166234047408
59 1692604114105553659010
60 3046687405389996586218
63 15228066033367763990128
64 24745607304222616483958
67 91353417175290660468884
68 134343260551898030101300
71 368674760966511746549004
72 491566347955348995398672
75 1007629118755817710057646
76 1219761564809674070069782
79 1873856945935044844028880
80 2061242640528549328431768
83 2377873706297857672084688
84 2377873706297857672084688
87 2061242640528549328431768
88 1873856945935044844028880
91 1219761564809674070069782
92 1007629118755817710057646
95 491566347955348995398672
96 368674760966511746549004
99 134343260551898030101300
100 91353417175290660468884
103 24745607304222616483958
104 15228066033367763990128
107 3046687405389996586218
108 1692604114105553659010
111 248066460166234047408
112 124033230083117023704
115 13179209289954805656
116 5907921405841809432
119 449320388493374440
120 179728155397349776
123 9630029630564070
124 3417107288264670
127 126530743283152
128 39540857275985
131 983150694636
132 268132007628
135 4493126316
136 1057206192
139 15108490
140 3021698
143 665328
144 110888
167 1

Crossrefs

Sequence in context: A251034 A265713 A114684 * A175535 A103874 A195223

Adjacent sequences: A146885 A146886 A146887 * A146889 A146890 A146891

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