Information on Result #737758
Linear OA(748, 61, F7, 33) (dual of [61, 13, 34]-code), using construction XX applied to C1 = C([0,51]), C2 = C([1,65]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,65]) 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(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 narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,65], and designed minimum distance d ≥ |I|+1 = 66 [i]
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using contraction [i] based on linear OA(789, 96, F7, 67) (dual of [96, 7, 68]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,65], and minimum distance d ≥ |{−1,0,…,65}|+1 = 68 (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(77, 12, F7, 6) (dual of [12, 5, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 14, F7, 6) (dual of [14, 7, 7]-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
None.