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A076710 Weight distribution of [137, 69, 21] binary quadratic-residue (or QR) code. 1
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51238, 270164, 409904, 1947044, 4057118, 17476816, 99448300, 390689750, 1445284240, 5203023264, 18055712240, 59809546795, 189973513945, 581095454420, 1709208146190 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,22
COMMENTS
Taken from the Tjhai-Tomlinson web site.
According to Boston and Hao, the Tjhai-Tomlinson web site gives several erroneous values, but their article with Ambroze and Ahmed has correct values. - Eric M. Schmidt, Nov 17 2017
LINKS
Nigel Boston and Jing Hao, The Weight Distribution of Quasi-quadratic Residue Codes, arXiv:1705.06413 [cs.IT], 2017.
C. Tjhai, M. Tomlinson, M. Ambroze, M. Ahmed, On the Weight Distribution of the Extended Quadratic Residue Code of Prime 137, arXiv:0801.3926 [cs.IT], 2008.
EXAMPLE
The weight distribution is:
i A_i
0 1
21 51238
22 270164
23 409904
24 1947044
25 4057118
26 17476816
27 99448300
28 390689750
29 1445284240
30 5203023264
31 18055712240
32 59809546795
33 189973513945
34 581095454420
35 1709208146190
36 4842756414205
37 13221982102853
38 34794689744350
39 88328700833460
40 216405317041977
41 511980845799941
42 1170241933257008
43 2585374360137184
44 5523299769383984
45 11414864729214318
46 22829729458428636
47 44202380361406672
48 82879463177637510
49 150535995889831600
50 264943352766103616
51 451961780387038844
52 747475252178564242
53 1198781830242451728
54 1864771735932702688
55 2814110491202421488
56 4120661790689260036
57 5855675469990794812
58 8076793751711441120
59 10814690610004223000
60 14059097793005489900
61 17746731937729182608
62 21754058504313191584
63 25897686719588958304
64 29944200269524733039
65 33629639551783390742
66 36686879511036426264
67 38877142978140092004
68 40020588359850094710
69 40020588359850094710
70 38877142978140092004
71 36686879511036426264
72 33629639551783390742
73 29944200269524733039
74 25897686719588958304
75 21754058504313191584
76 17746731937729182608
77 14059097793005489900
78 10814690610004223000
79 8076793751711441120
80 5855675469990794812
81 4120661790689260036
82 2814110491202421488
83 1864771735932702688
84 1198781830242451728
85 747475252178564242
86 451961780387038844
87 264943352766103616
88 150535995889831600
89 82879463177637510
90 44202380361406672
91 22829729458428636
92 11414864729214318
93 5523299769383984
94 2585374360137184
95 1170241933257008
96 511980845799941
97 216405317041977
98 88328700833460
99 34794689744350
100 13221982102853
101 4842756414205
102 1709208146190
103 581095454420
104 189973513945
105 59809546795
106 18055712240
107 5203023264
108 1445284240
109 390689750
110 99448300
111 17476816
112 4057118
113 1947044
114 409904
115 270164
116 51238
137 1
CROSSREFS
Cf. A097937.
Sequence in context: A252207 A206236 A233901 * A203405 A152512 A344644
KEYWORD
nonn,fini
AUTHOR
N. J. A. Sloane, Apr 14 2009
EXTENSIONS
Corrected (using the Tjhai et al. arXiv article) by Eric M. Schmidt, Nov 17 2017
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)