A106433 Weight distribution of [113,57,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3616, 22148, 0, 0, 79100, 371770, 539462, 2255932, 7723324, 28962465, 106963766, 362031208, 1164652580, 3577147210, 10584922440, 29637782832, 79257402672, 203097094347, 498291292415

Offset

0,16

Comments

Taken from the Tjhai-Tomlinson web site.

According to Boston and Hao, the Tjhai-Tomlinson tables give erroneous values for a(56) and a(57). The current version (v1) of their paper, however, contains an erroneous correction. - Eric M. Schmidt, Nov 08 2017

Links

Table of n, a(n) for n=0..33.

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
15 3616
16 22148
19 79100
20 371770
21 539462
22 2255932
23 7723324
24 28962465
25 106963766
26 362031208
27 1164652580
28 3577147210
29 10584922440
30 29637782832
31 79257402672
32 203097094347
33 498291292415
34 1172450099800
35 2645916266148
36 5732818576654
37 11930503538968
38 23861007077936
39 45892063616140
40 84900317689859
41 151162931905769
42 259136454695604
43 427856747425184
44 680681189085520
45 1043718121981906
46 1542887658581948
47 2199475409482456
48 3024278688038377
49 4011781195731400
50 5135079930536192
51 6343283392924660
52 7563145583871710
53 8704767791530440
54 9671964212811600
55 10375431209297308
56 10745982323915069
57 10745982323915069
58 10375431209297308
59 9671964212811600
60 8704767791530440
61 7563145583871710
62 6343283392924660
63 5135079930536192
64 4011781195731400
65 3024278688038377
66 2199475409482456
67 1542887658581948
68 1043718121981906
69 680681189085520
70 427856747425184
71 259136454695604
72 151162931905769
73 84900317689859
74 45892063616140
75 23861007077936
76 11930503538968
77 5732818576654
78 2645916266148
79 1172450099800
80 498291292415
81 203097094347
82 79257402672
83 29637782832
84 10584922440
85 3577147210
86 1164652580
87 362031208
88 106963766
89 28962465
90 7723324
91 2255932
92 539462
93 371770
94 79100
97 22148
98 3616
113 1

Crossrefs

Sequence in context: A045817 A107538 A270260 * A188309 A185495 A029829

Adjacent sequences: A106430 A106431 A106432 * A106434 A106435 A106436

Keyword

nonn,fini

Author

N. J. A. Sloane, Apr 11 2009

Extensions

In accordance with Boston and Hao, a(56) and a(57) corrected by Eric M. Schmidt, Nov 08 2017

Status

approved