Information on Result #727284
Linear OA(27105, 741, F27, 53) (dual of [741, 636, 54]-code), using construction XX applied to C1 = C([724,47]), C2 = C([0,48]), C3 = C1 + C2 = C([0,47]), and C∩ = C1 ∩ C2 = C([724,48]) based on
- linear OA(27100, 728, F27, 52) (dual of [728, 628, 53]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−4,−3,…,47}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2794, 728, F27, 49) (dual of [728, 634, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(27102, 728, F27, 53) (dual of [728, 626, 54]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−4,−3,…,48}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2792, 728, F27, 48) (dual of [728, 636, 49]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,47], and designed minimum distance d ≥ |I|+1 = 49 [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.