Information on Result #605052

Linear OA(73, 4, F7, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,7) or 4-cap in PG(2,7)), using dual of repetition code with length 4

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

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(722, 28, F7, 15) (dual of [28, 6, 16]-code) [i]Generalized (u, u+v)-Construction
2Linear OA(722, 28, F7, 15) (dual of [28, 6, 16]-code) [i]
3Linear OA(721, 28, F7, 14) (dual of [28, 7, 15]-code) [i]
4Linear OA(720, 28, F7, 13) (dual of [28, 8, 14]-code) [i]
5Linear OA(753, 16815, F7, 11) (dual of [16815, 16762, 12]-code) [i](u, u−v, u+v+w)-Construction
6Linear OA(771, 823551, F7, 11) (dual of [823551, 823480, 12]-code) [i]
7Linear OA(780, 5764809, F7, 11) (dual of [5764809, 5764729, 12]-code) [i]
8Linear OA(748, 16815, F7, 10) (dual of [16815, 16767, 11]-code) [i]
9Linear OA(764, 823551, F7, 10) (dual of [823551, 823487, 11]-code) [i]
10Linear OA(772, 5764809, F7, 10) (dual of [5764809, 5764737, 11]-code) [i]
11Linear OA(722, 348, F7, 7) (dual of [348, 326, 8]-code) [i]Construction X with Cyclic Codes
12Linear OA(728, 2406, F7, 7) (dual of [2406, 2378, 8]-code) [i]
13Linear OA(734, 16812, F7, 7) (dual of [16812, 16778, 8]-code) [i]
14Linear OA(740, 117654, F7, 7) (dual of [117654, 117614, 8]-code) [i]
15Linear OA(746, 823548, F7, 7) (dual of [823548, 823502, 8]-code) [i]
16Linear OA(752, 5764806, F7, 7) (dual of [5764806, 5764754, 8]-code) [i]
17Linear OA(750, 61, F7, 32) (dual of [61, 11, 33]-code) [i]
18Linear OA(763, 68, F7, 39) (dual of [68, 5, 40]-code) [i]
19Linear OA(774, 84, F7, 43) (dual of [84, 10, 44]-code) [i]
20Linear OA(775, 84, F7, 47) (dual of [84, 9, 48]-code) [i]
21Linear OA(7110, 2416, F7, 31) (dual of [2416, 2306, 32]-code) [i]Construction XX with a Chain of Cyclic Codes
22Linear OA(773, 2427, F7, 19) (dual of [2427, 2354, 20]-code) [i]
23Linear OA(762, 2416, F7, 17) (dual of [2416, 2354, 18]-code) [i]
24Linear OA(7102, 374, F7, 35) (dual of [374, 272, 36]-code) [i]
25Linear OA(793, 365, F7, 33) (dual of [365, 272, 34]-code) [i]
26Linear OA(784, 356, F7, 31) (dual of [356, 272, 32]-code) [i]
27Linear OA(766, 374, F7, 21) (dual of [374, 308, 22]-code) [i]
28Linear OA(757, 365, F7, 19) (dual of [365, 308, 20]-code) [i]
29Linear OA(748, 356, F7, 17) (dual of [356, 308, 18]-code) [i]
30Linear OA(755, 72, F7, 33) (dual of [72, 17, 34]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes
31Linear OA(753, 70, F7, 32) (dual of [70, 17, 33]-code) [i]
32Linear OA(748, 65, F7, 28) (dual of [65, 17, 29]-code) [i]
33Linear OA(744, 61, F7, 27) (dual of [61, 17, 28]-code) [i]
34Linear OA(741, 58, F7, 26) (dual of [58, 17, 27]-code) [i]
35Linear OA(756, 66, F7, 39) (dual of [66, 10, 40]-code) [i]Construction X with VarÅ¡amov Bound
36Linear OA(757, 67, F7, 40) (dual of [67, 10, 41]-code) [i]
37Linear OA(771, 80, F7, 50) (dual of [80, 9, 51]-code) [i]
38Linear OA(772, 81, F7, 51) (dual of [81, 9, 52]-code) [i]
39Linear OA(773, 82, F7, 52) (dual of [82, 9, 53]-code) [i]
40Linear OA(774, 83, F7, 53) (dual of [83, 9, 54]-code) [i]
41Linear OA(778, 87, F7, 56) (dual of [87, 9, 57]-code) [i]
42Linear OA(779, 88, F7, 57) (dual of [88, 9, 58]-code) [i]
43Linear OA(734, 65, F7, 19) (dual of [65, 31, 20]-code) [i]
44Linear OA(771, 91, F7, 45) (dual of [91, 20, 46]-code) [i]
45Linear OA(788, 104, F7, 59) (dual of [104, 16, 60]-code) [i]
46Linear OA(790, 105, F7, 61) (dual of [105, 15, 62]-code) [i]
47Linear OA(791, 104, F7, 63) (dual of [104, 13, 64]-code) [i]
48Linear OA(792, 105, F7, 64) (dual of [105, 13, 65]-code) [i]
49Linear OA(784, 103, F7, 55) (dual of [103, 19, 56]-code) [i]
50Linear OA(784, 105, F7, 54) (dual of [105, 21, 55]-code) [i]
51Linear OA(788, 103, F7, 60) (dual of [103, 15, 61]-code) [i]
52Linear OA(788, 105, F7, 59) (dual of [105, 17, 60]-code) [i]