A097937 Weight distribution of [138,69,22] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321402, 2356948, 21533934, 490138050, 6648307504, 77865259035, 771068968365, 6551964560395, 48016671847203, 304734017875437, 1682222779056949, 8108674129521168, 34244594187642954, 127081843539044182, 415479348655935216

Offset

0,12

Comments

Taken from the Tjhai-Tomlinson website. [This refers to the second table, which is not correct. The first table is correct and taken from the arXiv article.]

The arXiv article provides a corrected table, see link. - Hugo Pfoertner, Mar 11 2020

Links

Table of n, a(n) for n=0..25.

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

C. Tjhai, M. Tomlinson, M. Ambroze, and M. Ahmed, On the Weight Distribution of the Extended Quadratic Residue Code of Prime 137, arXiv:0801.3926 [cs.IT], 25 Jan 2008.

C. Tjhai, M. Tomlinson, M. Ambroze, and M. Ahmed, 3rd column of Table 1 of arXiv:0801.3926, 2008.

Example

The weight distribution as given in the arXiv:0801.3926 article:
i                     A_i
0                       1
22                 321402
24                2356948
26               21533934
28              490138050
30             6648307504
32            77865259035
34           771068968365
36          6551964560395
38         48016671847203
40        304734017875437
42       1682222779056949
44       8108674129521168
46      34244594187642954
48     127081843539044182
50     415479348655935216
52    1199437032565603086
54    3063553566175154416
56    6934772281891681524
58   13932469221702235932
60   24873788403009712900
62   39500790442042374192
64   55841886989113691343
66   70316519062819817006
68   78897731337990186714
70   78897731337990186714
72   70316519062819817006
74   55841886989113691343
76   39500790442042374192
78   24873788403009712900
80   13932469221702235932
82    6934772281891681524
84    3063553566175154416
86    1199437032565603086
88     415479348655935216
90     127081843539044182
92      34244594187642954
94       8108674129521168
96       1682222779056949
98        304734017875437
100        48016671847203
102         6551964560395
104          771068968365
106           77865259035
108            6648307504
110             490138050
112              21533934
114               2356948
116                321402
118                     1
---
The following version, which was taken from the website of the authors, *is not correct*. It is given here in accordance with the OEIS policy of including incorrect versions if they were previously published on the OEIS.
i A_i
0  1
22 321402
24 2356948
26 21533934
28 490138050
30 6648307504
32 77865259035
34 771068968365
36 6551964560395
38 48016671847203
40 304734017875437
42 1682222779056949
44 8108674129521168
46 34244594187642952
48 127081843539044176
50 415479348655935232
52 1199437032565603072
54 3063553566175154176
56 6934772281891681280
58 13932469221702236160
60 24873788403009712128
62 39500790442042376192
64 55841886989113688064
66 70316519062819815424
68 78897731337990193152
70 78897731337990193152
72 70316519062819815424
74 55841886989113688064
76 39500790442042376192
78 24873788403009712128
80 13932469221702236160
82 6934772281891681280
84 3063553566175154176
86 1199437032565603072
88 415479348655935232
90 127081843539044176
92 34244594187642952
94 8108674129521168
96 1682222779056949
98 304734017875437
100 48016671847203
102 6551964560395
104 771068968365
106 77865259035
108 6648307504
110 490138050
112 21533934
114 2356948
116 321402
118 1

Crossrefs

Cf. A076710.

Sequence in context: A236318 A348827 A348697 * A244565 A362874 A186880

Adjacent sequences: A097934 A097935 A097936 * A097938 A097939 A097940

Keyword

nonn,fini

Author

N. J. A. Sloane, Apr 02 2009

Extensions

At the suggestion of Hugo Pfoertner, corrected by Peter Luschny, Mar 13 2020

Status

approved