Information on Result #605051
Linear OA(72, 3, F7, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,7)), using dual of repetition code with length 3
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(714, 18, F7, 11) (dual of [18, 4, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 2 | Linear OA(714, 18, F7, 11) (dual of [18, 4, 12]-code) | [i] | ||
| 3 | Linear OA(754, 16816, F7, 11) (dual of [16816, 16762, 12]-code) | [i] | ||
| 4 | Linear OA(772, 823552, F7, 11) (dual of [823552, 823480, 12]-code) | [i] | ||
| 5 | Linear OA(781, 5764810, F7, 11) (dual of [5764810, 5764729, 12]-code) | [i] | ||
| 6 | Linear OA(736, 16813, F7, 8) (dual of [16813, 16777, 9]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 7 | Linear OA(742, 117655, F7, 8) (dual of [117655, 117613, 9]-code) | [i] | ||
| 8 | Linear OA(748, 823549, F7, 8) (dual of [823549, 823501, 9]-code) | [i] | ||
| 9 | Linear OA(754, 5764807, F7, 8) (dual of [5764807, 5764753, 9]-code) | [i] | ||
| 10 | Linear OA(719, 2405, F7, 5) (dual of [2405, 2386, 6]-code) | [i] | Construction X with Cyclic Codes | |
| 11 | Linear OA(723, 16811, F7, 5) (dual of [16811, 16788, 6]-code) | [i] | ||
| 12 | Linear OA(727, 117653, F7, 5) (dual of [117653, 117626, 6]-code) | [i] | ||
| 13 | Linear OA(731, 823547, F7, 5) (dual of [823547, 823516, 6]-code) | [i] | ||
| 14 | Linear OA(735, 5764805, F7, 5) (dual of [5764805, 5764770, 6]-code) | [i] | ||
| 15 | Linear OA(715, 53, F7, 7) (dual of [53, 38, 8]-code) | [i] | ||
| 16 | Linear OA(732, 39, F7, 14) (dual of [39, 7, 15]-code) | [i] | ||
| 17 | Linear OA(773, 177, F7, 14) (dual of [177, 104, 15]-code) | [i] | ||
| 18 | Linear OA(7108, 351, F7, 14) (dual of [351, 243, 15]-code) | [i] | ||
| 19 | Linear OA(739, 60, F7, 21) (dual of [60, 21, 22]-code) | [i] | ||
| 20 | Linear OA(740, 60, F7, 24) (dual of [60, 20, 25]-code) | [i] | ||
| 21 | Linear OA(743, 60, F7, 25) (dual of [60, 17, 26]-code) | [i] | ||
| 22 | Linear OA(762, 123, F7, 25) (dual of [123, 61, 26]-code) | [i] | ||
| 23 | Linear OA(746, 60, F7, 26) (dual of [60, 14, 27]-code) | [i] | ||
| 24 | Linear OA(766, 123, F7, 26) (dual of [123, 57, 27]-code) | [i] | ||
| 25 | Linear OA(772, 123, F7, 28) (dual of [123, 51, 29]-code) | [i] | ||
| 26 | Linear OA(756, 63, F7, 35) (dual of [63, 7, 36]-code) | [i] | ||
| 27 | Linear OA(786, 123, F7, 35) (dual of [123, 37, 36]-code) | [i] | ||
| 28 | Linear OA(767, 75, F7, 38) (dual of [75, 8, 39]-code) | [i] | ||
| 29 | Linear OA(768, 75, F7, 41) (dual of [75, 7, 42]-code) | [i] | ||
| 30 | Linear OA(790, 123, F7, 42) (dual of [123, 33, 43]-code) | [i] | ||
| 31 | Linear OA(791, 123, F7, 45) (dual of [123, 32, 46]-code) | [i] | ||
| 32 | Linear OA(799, 123, F7, 47) (dual of [123, 24, 48]-code) | [i] | ||
| 33 | Linear OA(770, 75, F7, 50) (dual of [75, 5, 51]-code) | [i] | ||
| 34 | Linear OA(7105, 123, F7, 52) (dual of [123, 18, 53]-code) | [i] | ||
| 35 | Linear OA(771, 75, F7, 53) (dual of [75, 4, 54]-code) | [i] | ||
| 36 | Linear OA(7107, 123, F7, 53) (dual of [123, 16, 54]-code) | [i] | ||
| 37 | Linear OA(790, 103, F7, 55) (dual of [103, 13, 56]-code) | [i] | ||
| 38 | Linear OA(7108, 117, F7, 78) (dual of [117, 9, 79]-code) | [i] | ||
| 39 | Linear OA(7109, 117, F7, 81) (dual of [117, 8, 82]-code) | [i] | ||
| 40 | Linear OA(7110, 119, F7, 80) (dual of [119, 9, 81]-code) | [i] | Construction XX with Cyclic Codes | |
| 41 | Linear OA(747, 67, F7, 26) (dual of [67, 20, 27]-code) | [i] | ||
| 42 | Linear OA(746, 67, F7, 25) (dual of [67, 21, 26]-code) | [i] | ||
| 43 | Linear OA(743, 63, F7, 25) (dual of [63, 20, 26]-code) | [i] | ||
| 44 | Linear OA(742, 63, F7, 24) (dual of [63, 21, 25]-code) | [i] | ||
| 45 | Linear OA(742, 63, F7, 24) (dual of [63, 21, 25]-code) | [i] | ||
| 46 | Linear OA(7109, 118, F7, 79) (dual of [118, 9, 80]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 47 | Linear OA(740, 61, F7, 22) (dual of [61, 21, 23]-code) | [i] | ||
| 48 | Linear OA(752, 125, F7, 22) (dual of [125, 73, 23]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 49 | Linear OA(745, 71, F7, 24) (dual of [71, 26, 25]-code) | [i] | ||
| 50 | Linear OA(738, 64, F7, 20) (dual of [64, 26, 21]-code) | [i] | ||
| 51 | Linear OA(734, 60, F7, 19) (dual of [60, 26, 20]-code) | [i] | ||
| 52 | Linear OA(719, 36, F7, 12) (dual of [36, 17, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 53 | Linear OA(759, 69, F7, 41) (dual of [69, 10, 42]-code) | [i] | ||
| 54 | Linear OA(761, 84, F7, 37) (dual of [84, 23, 38]-code) | [i] | ||
| 55 | Linear OA(772, 92, F7, 46) (dual of [92, 20, 47]-code) | [i] | ||
| 56 | Linear OA(782, 103, F7, 52) (dual of [103, 21, 53]-code) | [i] | ||
| 57 | Linear OA(783, 104, F7, 53) (dual of [104, 21, 54]-code) | [i] | ||
| 58 | Linear OA(784, 104, F7, 54) (dual of [104, 20, 55]-code) | [i] | ||
| 59 | Linear OA(785, 104, F7, 55) (dual of [104, 19, 56]-code) | [i] | ||
| 60 | Linear OA(786, 103, F7, 57) (dual of [103, 17, 58]-code) | [i] | ||
| 61 | Linear OA(787, 104, F7, 58) (dual of [104, 17, 59]-code) | [i] | ||
| 62 | Linear OA(781, 102, F7, 52) (dual of [102, 21, 53]-code) | [i] | ||