Information on Result #685954
Linear OA(738, 51, F7, 27) (dual of [51, 13, 28]-code), using construction XX applied to C1 = C([0,51]), C2 = C([1,53]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,53]) based on
- linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using contraction [i] based on linear OA(784, 96, F7, 53) (dual of [96, 12, 54]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,51], and minimum distance d ≥ |{−1,0,…,51}|+1 = 54 (BCH-bound) [i]
- linear OA(737, 48, F7, 26) (dual of [48, 11, 27]-code), using contraction [i] based on linear OA(785, 96, F7, 53) (dual of [96, 11, 54]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using contraction [i] based on linear OA(786, 96, F7, 55) (dual of [96, 10, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,53], and minimum distance d ≥ |{−1,0,…,53}|+1 = 56 (BCH-bound) [i]
- linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using contraction [i] based on linear OA(783, 96, F7, 51) (dual of [96, 13, 52]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-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 OOA(738, 17, F7, 3, 27) (dual of [(17, 3), 13, 28]-NRT-code) | [i] | OOA Folding | |