Information on Result #685925
Linear OA(756, 65, F7, 41) (dual of [65, 9, 42]-code), using construction XX applied to C1 = C([0,63]), C2 = C([1,81]), C3 = C1 + C2 = C([1,63]), and C∩ = C1 ∩ C2 = C([0,81]) based on
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using contraction [i] based on linear OA(788, 96, F7, 65) (dual of [96, 8, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,63], and minimum distance d ≥ |{−1,0,…,63}|+1 = 66 (BCH-bound) [i]
- linear OA(745, 48, F7, 40) (dual of [48, 3, 41]-code), using contraction [i] based on linear OA(793, 96, F7, 81) (dual of [96, 3, 82]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,81], and designed minimum distance d ≥ |I|+1 = 82 [i]
- linear OA(746, 48, F7, 41) (dual of [48, 2, 42]-code), using contraction [i] based on linear OA(794, 96, F7, 83) (dual of [96, 2, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,81], and minimum distance d ≥ |{15,32,49,…,−31}|+1 = 84 (BCH-bound) [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(787, 96, F7, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(710, 16, F7, 8) (dual of [16, 6, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), 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, 65, F7, 40) (dual of [65, 9, 41]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(756, 65, F7, 39) (dual of [65, 9, 40]-code) | [i] | ||
| 3 | Linear OA(759, 69, F7, 41) (dual of [69, 10, 42]-code) | [i] | Construction X with Varšamov Bound | |