Information on Result #727099
Linear OA(2787, 741, F27, 44) (dual of [741, 654, 45]-code), using construction XX applied to C1 = C([724,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([724,39]) based on
- linear OA(2782, 728, F27, 43) (dual of [728, 646, 44]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2776, 728, F27, 40) (dual of [728, 652, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2784, 728, F27, 44) (dual of [728, 644, 45]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−4,−3,…,39}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(273, 11, F27, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,27) or 11-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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.
Other Results with Identical Parameters
None.
Depending Results
None.