Information on Result #606802

Linear OA(76, 8, F7, 6) (dual of [8, 2, 7]-code or 8-arc in PG(5,7)), using extended Reed–Solomon code RSe(2,7)

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(7110, 112, F7, 97) (dual of [112, 2, 98]-code) [i]Repeating Each Code Word
2Linear OA(7102, 104, F7, 90) (dual of [104, 2, 91]-code) [i]
3Linear OA(794, 96, F7, 83) (dual of [96, 2, 84]-code) [i]
4Linear OA(786, 88, F7, 76) (dual of [88, 2, 77]-code) [i]
5Linear OA(778, 80, F7, 69) (dual of [80, 2, 70]-code) [i]
6Linear OA(770, 72, F7, 62) (dual of [72, 2, 63]-code) [i]
7Linear OA(762, 64, F7, 55) (dual of [64, 2, 56]-code) [i]
8Linear OA(738, 40, F7, 34) (dual of [40, 2, 35]-code) [i]
9Linear OA(730, 32, F7, 27) (dual of [32, 2, 28]-code) [i]
10Linear OA(722, 24, F7, 20) (dual of [24, 2, 21]-code) [i]
11Linear OA(714, 16, F7, 13) (dual of [16, 2, 14]-code) [i]
12Linear OA(740, 351, F7, 13) (dual of [351, 311, 14]-code) [i](u, u+v)-Construction
13Linear OA(762, 16815, F7, 13) (dual of [16815, 16753, 14]-code) [i]
14Linear OA(773, 117657, F7, 13) (dual of [117657, 117584, 14]-code) [i]
15Linear OA(784, 823551, F7, 13) (dual of [823551, 823467, 14]-code) [i]
16Linear OA(795, 5764809, F7, 13) (dual of [5764809, 5764714, 14]-code) [i]
17Linear OA(737, 351, F7, 12) (dual of [351, 314, 13]-code) [i]
18Linear OA(757, 16815, F7, 12) (dual of [16815, 16758, 13]-code) [i]
19Linear OA(767, 117657, F7, 12) (dual of [117657, 117590, 13]-code) [i]
20Linear OA(777, 823551, F7, 12) (dual of [823551, 823474, 13]-code) [i]
21Linear OA(787, 5764809, F7, 12) (dual of [5764809, 5764722, 13]-code) [i]
22Linear OA(747, 56, F7, 34) (dual of [56, 9, 35]-code) [i]Generalized (u, u+v)-Construction
23Linear OA(750, 60, F7, 34) (dual of [60, 10, 35]-code) [i]
24Linear OA(742, 56, F7, 27) (dual of [56, 14, 28]-code) [i]
25Linear OA(744, 59, F7, 26) (dual of [59, 15, 27]-code) [i]
26Linear OA(734, 56, F7, 19) (dual of [56, 22, 20]-code) [i]
27Linear OA(737, 60, F7, 19) (dual of [60, 23, 20]-code) [i]
28Linear OA(7108, 112, F7, 90) (dual of [112, 4, 91]-code) [i]Concatenation of Two Codes
29Linear OA(7100, 16823, F7, 20) (dual of [16823, 16723, 21]-code) [i](u, u−v, u+v+w)-Construction
30Linear OA(7102, 16826, F7, 20) (dual of [16826, 16724, 21]-code) [i]
31Linear OA(795, 16824, F7, 19) (dual of [16824, 16729, 20]-code) [i]
32Linear OA(796, 16826, F7, 19) (dual of [16826, 16730, 20]-code) [i]
33Linear OA(790, 16823, F7, 18) (dual of [16823, 16733, 19]-code) [i]
34Linear OA(766, 16823, F7, 13) (dual of [16823, 16757, 14]-code) [i]
35Linear OA(788, 823559, F7, 13) (dual of [823559, 823471, 14]-code) [i]
36Linear OA(744, 65, F7, 24) (dual of [65, 21, 25]-code) [i]Construction X with Cyclic Codes
37Linear OA(753, 64, F7, 35) (dual of [64, 11, 36]-code) [i]Construction XX with Cyclic Codes
38Linear OA(778, 187, F7, 32) (dual of [187, 109, 33]-code) [i]
39Linear OA(760, 65, F7, 48) (dual of [65, 5, 49]-code) [i]Construction X with De Boer–Brouwer Codes
40Linear OA(7101, 110, F7, 73) (dual of [110, 9, 74]-code) [i]Construction X with VarÅ¡amov Bound
41Linear OA(7102, 111, F7, 74) (dual of [111, 9, 75]-code) [i]
42Linear OA(7103, 112, F7, 75) (dual of [112, 9, 76]-code) [i]
43Linear OA(7104, 113, F7, 76) (dual of [113, 9, 77]-code) [i]
44Linear OA(7106, 115, F7, 77) (dual of [115, 9, 78]-code) [i]
45Linear OA(7107, 116, F7, 78) (dual of [116, 9, 79]-code) [i]
46Linear OA(795, 106, F7, 67) (dual of [106, 11, 68]-code) [i]
47Linear OA(796, 106, F7, 69) (dual of [106, 10, 70]-code) [i]
48Linear OA(799, 109, F7, 71) (dual of [109, 10, 72]-code) [i]
49Linear OA(799, 110, F7, 70) (dual of [110, 11, 71]-code) [i]
50Linear OA(7100, 110, F7, 72) (dual of [110, 10, 73]-code) [i]