Information on Result #685937
Linear OA(752, 65, F7, 34) (dual of [65, 13, 35]-code), using construction XX applied to C1 = C([0,51]), C2 = C([1,67]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,67]) 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(742, 48, F7, 33) (dual of [48, 6, 34]-code), using contraction [i] based on linear OA(790, 96, F7, 67) (dual of [96, 6, 68]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
- linear OA(743, 48, F7, 34) (dual of [48, 5, 35]-code), using contraction [i] based on linear OA(791, 96, F7, 69) (dual of [96, 5, 70]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,67], and minimum distance d ≥ |{−1,0,…,67}|+1 = 70 (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(79, 16, F7, 7) (dual of [16, 7, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-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.