Information on Result #622077
Linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using construction X applied to C1 ⊂ C0 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(745, 355, F7, 15) (dual of [355, 310, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(757, 2413, F7, 15) (dual of [2413, 2356, 16]-code) | [i] | ||
| 3 | Linear OA(769, 16819, F7, 15) (dual of [16819, 16750, 16]-code) | [i] | ||
| 4 | Linear OA(781, 117661, F7, 15) (dual of [117661, 117580, 16]-code) | [i] | ||
| 5 | Linear OA(793, 823555, F7, 15) (dual of [823555, 823462, 16]-code) | [i] | ||
| 6 | Linear OA(7105, 5764813, F7, 15) (dual of [5764813, 5764708, 16]-code) | [i] | ||
| 7 | Linear OA(76, 11, F7, 5) (dual of [11, 5, 6]-code) | [i] | Construction for [s, s−6, 6]-Code from [s, 3, s−3]-Code | |
| 8 | Linear OA(758, 68, F7, 40) (dual of [68, 10, 41]-code) | [i] | Construction X with Cyclic Codes | |
| 9 | Linear OA(756, 67, F7, 37) (dual of [67, 11, 38]-code) | [i] | Construction XX with Cyclic Codes | |
| 10 | Linear OA(763, 70, F7, 47) (dual of [70, 7, 48]-code) | [i] | ||
| 11 | Linear OA(763, 70, F7, 47) (dual of [70, 7, 48]-code) | [i] | ||
| 12 | Linear OA(760, 67, F7, 45) (dual of [67, 7, 46]-code) | [i] | ||