Information on Result #625168
Linear OA(76, 11, F7, 5) (dual of [11, 5, 6]-code), using construction for [s, s−6, 6]-code from [s, 3, s−3]-code based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(752, 16818, F7, 11) (dual of [16818, 16766, 12]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(761, 117660, F7, 11) (dual of [117660, 117599, 12]-code) | [i] | ||
| 3 | Linear OA(770, 823554, F7, 11) (dual of [823554, 823484, 12]-code) | [i] | ||
| 4 | Linear OA(779, 5764812, F7, 11) (dual of [5764812, 5764733, 12]-code) | [i] | ||
| 5 | Linear OA(747, 16818, F7, 10) (dual of [16818, 16771, 11]-code) | [i] | ||
| 6 | Linear OA(755, 117660, F7, 10) (dual of [117660, 117605, 11]-code) | [i] | ||
| 7 | Linear OA(763, 823554, F7, 10) (dual of [823554, 823491, 11]-code) | [i] | ||
| 8 | Linear OA(771, 5764812, F7, 10) (dual of [5764812, 5764741, 11]-code) | [i] | ||
| 9 | Linear OA(771, 76, F7, 54) (dual of [76, 5, 55]-code) | [i] | Juxtaposition | |
| 10 | Linear OA(751, 59, F7, 38) (dual of [59, 8, 39]-code) | [i] | Construction X with Cyclic Codes | |
| 11 | Linear OA(746, 59, F7, 31) (dual of [59, 13, 32]-code) | [i] | ||
| 12 | Linear OA(750, 59, F7, 37) (dual of [59, 9, 38]-code) | [i] | ||
| 13 | Linear OA(746, 66, F7, 27) (dual of [66, 20, 28]-code) | [i] | Construction XX with Cyclic Codes | |
| 14 | Linear OA(748, 67, F7, 28) (dual of [67, 19, 29]-code) | [i] | ||
| 15 | Linear OA(749, 77, F7, 25) (dual of [77, 28, 26]-code) | [i] | ||
| 16 | Linear OA(749, 67, F7, 29) (dual of [67, 18, 30]-code) | [i] | ||
| 17 | Linear OA(754, 67, F7, 35) (dual of [67, 13, 36]-code) | [i] | ||
| 18 | Linear OA(755, 66, F7, 37) (dual of [66, 11, 38]-code) | [i] | ||
| 19 | Linear OA(756, 67, F7, 38) (dual of [67, 11, 39]-code) | [i] | ||
| 20 | Linear OA(759, 67, F7, 43) (dual of [67, 8, 44]-code) | [i] | ||
| 21 | Linear OA(774, 187, F7, 30) (dual of [187, 113, 31]-code) | [i] | ||
| 22 | Linear OA(773, 185, F7, 30) (dual of [185, 112, 31]-code) | [i] | ||
| 23 | Linear OA(752, 60, F7, 39) (dual of [60, 8, 40]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 24 | Linear OA(747, 60, F7, 32) (dual of [60, 13, 33]-code) | [i] | ||
| 25 | Linear OA(751, 60, F7, 38) (dual of [60, 9, 39]-code) | [i] | ||
| 26 | Linear OA(746, 60, F7, 31) (dual of [60, 14, 32]-code) | [i] | ||
| 27 | Linear OA(733, 63, F7, 17) (dual of [63, 30, 18]-code) | [i] | ||
| 28 | Linear OA(773, 183, F7, 30) (dual of [183, 110, 31]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 29 | Linear OA(770, 183, F7, 29) (dual of [183, 113, 30]-code) | [i] | ||
| 30 | Linear OA(753, 126, F7, 22) (dual of [126, 73, 23]-code) | [i] | ||
| 31 | Linear OA(742, 60, F7, 26) (dual of [60, 18, 27]-code) | [i] | ||
| 32 | Linear OA(740, 60, F7, 25) (dual of [60, 20, 26]-code) | [i] | ||
| 33 | Linear OA(739, 60, F7, 24) (dual of [60, 21, 25]-code) | [i] | ||
| 34 | Linear OA(7101, 110, F7, 72) (dual of [110, 9, 73]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 35 | Linear OA(752, 61, F7, 39) (dual of [61, 9, 40]-code) | [i] | ||
| 36 | Linear OA(747, 61, F7, 32) (dual of [61, 14, 33]-code) | [i] | ||