Information on Result #606800

Linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using extended Reed–Solomon code RSe(4,7)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(726, 351, F7, 9) (dual of [351, 325, 10]-code) [i](u, u+v)-Construction
2Linear OA(733, 2409, F7, 9) (dual of [2409, 2376, 10]-code) [i]
3Linear OA(740, 16815, F7, 9) (dual of [16815, 16775, 10]-code) [i]
4Linear OA(747, 117657, F7, 9) (dual of [117657, 117610, 10]-code) [i]
5Linear OA(754, 823551, F7, 9) (dual of [823551, 823497, 10]-code) [i]
6Linear OA(761, 5764809, F7, 9) (dual of [5764809, 5764748, 10]-code) [i]
7Linear OA(723, 351, F7, 8) (dual of [351, 328, 9]-code) [i]
8Linear OA(729, 2409, F7, 8) (dual of [2409, 2380, 9]-code) [i]
9Linear OA(735, 16815, F7, 8) (dual of [16815, 16780, 9]-code) [i]
10Linear OA(741, 117657, F7, 8) (dual of [117657, 117616, 9]-code) [i]
11Linear OA(747, 823551, F7, 8) (dual of [823551, 823504, 9]-code) [i]
12Linear OA(753, 5764809, F7, 8) (dual of [5764809, 5764756, 9]-code) [i]
13Linear OA(747, 56, F7, 34) (dual of [56, 9, 35]-code) [i]Generalized (u, u+v)-Construction
14Linear OA(750, 60, F7, 34) (dual of [60, 10, 35]-code) [i]
15Linear OA(744, 56, F7, 29) (dual of [56, 12, 30]-code) [i]
16Linear OA(744, 56, F7, 29) (dual of [56, 12, 30]-code) [i]
17Linear OA(742, 56, F7, 27) (dual of [56, 14, 28]-code) [i]
18Linear OA(744, 59, F7, 26) (dual of [59, 15, 27]-code) [i]
19Linear OA(734, 56, F7, 19) (dual of [56, 22, 20]-code) [i]
20Linear OA(737, 60, F7, 19) (dual of [60, 23, 20]-code) [i]
21Linear OA(754, 58, F7, 46) (dual of [58, 4, 47]-code) [i]Juxtaposition
22Linear OA(761, 65, F7, 50) (dual of [65, 4, 51]-code) [i]
23Linear OA(762, 66, F7, 51) (dual of [66, 4, 52]-code) [i]
24Linear OA(7104, 108, F7, 88) (dual of [108, 4, 89]-code) [i]
25Linear OA(762, 66, F7, 52) (dual of [66, 4, 53]-code) [i]
26Linear OA(764, 68, F7, 53) (dual of [68, 4, 54]-code) [i]
27Linear OA(771, 16823, F7, 14) (dual of [16823, 16752, 15]-code) [i](u, u−v, u+v+w)-Construction
28Linear OA(795, 823559, F7, 14) (dual of [823559, 823464, 15]-code) [i]
29Linear OA(766, 16823, F7, 13) (dual of [16823, 16757, 14]-code) [i]
30Linear OA(788, 823559, F7, 13) (dual of [823559, 823471, 14]-code) [i]
31Linear OA(744, 56, F7, 31) (dual of [56, 12, 32]-code) [i]Construction X with Cyclic Codes
32Linear OA(748, 56, F7, 37) (dual of [56, 8, 38]-code) [i]
33Linear OA(743, 56, F7, 30) (dual of [56, 13, 31]-code) [i]
34Linear OA(742, 65, F7, 22) (dual of [65, 23, 23]-code) [i]
35Linear OA(741, 65, F7, 21) (dual of [65, 24, 22]-code) [i]
36Linear OA(729, 58, F7, 16) (dual of [58, 29, 17]-code) [i]
37Linear OA(749, 57, F7, 38) (dual of [57, 8, 39]-code) [i]Construction XX with Cyclic Codes
38Linear OA(744, 57, F7, 31) (dual of [57, 13, 32]-code) [i]
39Linear OA(743, 67, F7, 22) (dual of [67, 24, 23]-code) [i]
40Linear OA(732, 60, F7, 18) (dual of [60, 28, 19]-code) [i]
41Linear OA(735, 63, F7, 19) (dual of [63, 28, 20]-code) [i]
42Linear OA(739, 67, F7, 20) (dual of [67, 28, 21]-code) [i]
43Linear OA(737, 64, F7, 20) (dual of [64, 27, 21]-code) [i]
44Linear OA(741, 68, F7, 21) (dual of [68, 27, 22]-code) [i]
45Linear OA(743, 63, F7, 26) (dual of [63, 20, 27]-code) [i]
46Linear OA(742, 61, F7, 26) (dual of [61, 19, 27]-code) [i]
47Linear OA(745, 64, F7, 27) (dual of [64, 19, 28]-code) [i]
48Linear OA(745, 74, F7, 23) (dual of [74, 29, 24]-code) [i]
49Linear OA(747, 76, F7, 24) (dual of [76, 29, 25]-code) [i]
50Linear OA(744, 72, F7, 23) (dual of [72, 28, 24]-code) [i]
51Linear OA(746, 74, F7, 24) (dual of [74, 28, 25]-code) [i]
52Linear OA(741, 67, F7, 22) (dual of [67, 26, 23]-code) [i]
53Linear OA(752, 72, F7, 30) (dual of [72, 20, 31]-code) [i]
54Linear OA(751, 70, F7, 30) (dual of [70, 19, 31]-code) [i]
55Linear OA(749, 67, F7, 29) (dual of [67, 18, 30]-code) [i]
56Linear OA(749, 66, F7, 30) (dual of [66, 17, 31]-code) [i]
57Linear OA(747, 64, F7, 29) (dual of [64, 17, 30]-code) [i]
58Linear OA(747, 64, F7, 29) (dual of [64, 17, 30]-code) [i]
59Linear OA(757, 70, F7, 37) (dual of [70, 13, 38]-code) [i]
60Linear OA(754, 67, F7, 35) (dual of [67, 13, 36]-code) [i]
61Linear OA(756, 67, F7, 37) (dual of [67, 11, 38]-code) [i]
62Linear OA(756, 68, F7, 37) (dual of [68, 12, 38]-code) [i]
63Linear OA(754, 66, F7, 36) (dual of [66, 12, 37]-code) [i]
64Linear OA(752, 64, F7, 35) (dual of [64, 12, 36]-code) [i]
65Linear OA(752, 64, F7, 35) (dual of [64, 12, 36]-code) [i]
66Linear OA(753, 64, F7, 36) (dual of [64, 11, 37]-code) [i]
67Linear OA(753, 63, F7, 37) (dual of [63, 10, 38]-code) [i]
68Linear OA(761, 69, F7, 44) (dual of [69, 8, 45]-code) [i]
69Linear OA(762, 70, F7, 45) (dual of [70, 8, 46]-code) [i]
70Linear OA(759, 67, F7, 43) (dual of [67, 8, 44]-code) [i]
71Linear OA(753, 128, F7, 22) (dual of [128, 75, 23]-code) [i]
72Linear OA(752, 126, F7, 22) (dual of [126, 74, 23]-code) [i]
73Linear OA(756, 130, F7, 23) (dual of [130, 74, 24]-code) [i]
74Linear OA(791, 187, F7, 39) (dual of [187, 96, 40]-code) [i]
75Linear OA(7106, 187, F7, 46) (dual of [187, 81, 47]-code) [i]
76Linear OA(768, 180, F7, 28) (dual of [180, 112, 29]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
77Linear OA(737, 57, F7, 24) (dual of [57, 20, 25]-code) [i]
78Linear OA(731, 57, F7, 18) (dual of [57, 26, 19]-code) [i]
79Linear OA(729, 57, F7, 17) (dual of [57, 28, 18]-code) [i]
80Linear OA(769, 181, F7, 29) (dual of [181, 112, 30]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes
81Linear OA(764, 77, F7, 40) (dual of [77, 13, 41]-code) [i]
82Linear OA(763, 76, F7, 40) (dual of [76, 13, 41]-code) [i]
83Linear OA(739, 58, F7, 25) (dual of [58, 19, 26]-code) [i]