Information on Result #712458
Linear OA(747, 73, F7, 25) (dual of [73, 26, 26]-code), using construction XX applied to C1 = C([5,24]), C2 = C([0,16]), C3 = C1 + C2 = C([5,16]), and C∩ = C1 ∩ C2 = C([0,24]) based on
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {5,6,…,24}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(725, 48, F7, 17) (dual of [48, 23, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(720, 48, F7, 12) (dual of [48, 28, 13]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {5,6,…,16}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(79, 18, F7, 7) (dual of [18, 9, 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
- linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
- Reed–Solomon code RS(3,7) [i]
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.