Information on Result #614234
Linear OA(76, 10, F7, 5) (dual of [10, 4, 6]-code), using construction X applied to C([0,2]) ⊂ C([1,2]) based on
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(74, 8, F7, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,7)), using the narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [1,2], and minimum distance d ≥ |{1,2}| + |{−3,0}| = 4 (simple Roos-bound) [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 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(756, 60, F7, 47) (dual of [60, 4, 48]-code) | [i] | Juxtaposition | |
| 2 | Linear OA(764, 68, F7, 52) (dual of [68, 4, 53]-code) | [i] | ||
| 3 | Linear OA(7106, 110, F7, 89) (dual of [110, 4, 90]-code) | [i] | ||
| 4 | Linear OA(746, 58, F7, 32) (dual of [58, 12, 33]-code) | [i] | Construction X with Cyclic Codes | |
| 5 | Linear OA(750, 58, F7, 38) (dual of [58, 8, 39]-code) | [i] | ||
| 6 | Linear OA(745, 58, F7, 31) (dual of [58, 13, 32]-code) | [i] | ||
| 7 | Linear OA(744, 67, F7, 23) (dual of [67, 23, 24]-code) | [i] | ||
| 8 | Linear OA(731, 60, F7, 17) (dual of [60, 29, 18]-code) | [i] | ||
| 9 | Linear OA(751, 59, F7, 39) (dual of [59, 8, 40]-code) | [i] | Construction XX with Cyclic Codes | |
| 10 | Linear OA(746, 59, F7, 32) (dual of [59, 13, 33]-code) | [i] | ||
| 11 | Linear OA(754, 74, F7, 31) (dual of [74, 20, 32]-code) | [i] | ||
| 12 | Linear OA(749, 66, F7, 30) (dual of [66, 17, 31]-code) | [i] | ||
| 13 | Linear OA(759, 72, F7, 38) (dual of [72, 13, 39]-code) | [i] | ||
| 14 | Linear OA(754, 66, F7, 36) (dual of [66, 12, 37]-code) | [i] | ||
| 15 | Linear OA(773, 184, F7, 30) (dual of [184, 111, 31]-code) | [i] | ||
| 16 | Linear OA(777, 188, F7, 31) (dual of [188, 111, 32]-code) | [i] | ||
| 17 | Linear OA(748, 59, F7, 33) (dual of [59, 11, 34]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 18 | Linear OA(748, 60, F7, 33) (dual of [60, 12, 34]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |