Information on Result #725850
Linear OA(2760, 763, F27, 25) (dual of [763, 703, 26]-code), using construction XX applied to C1 = C([3,24]), C2 = C([0,14]), C3 = C1 + C2 = C([3,14]), and C∩ = C1 ∩ C2 = C([0,24]) based on
- linear OA(2744, 728, F27, 22) (dual of [728, 684, 23]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {3,4,…,24}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2729, 728, F27, 15) (dual of [728, 699, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2724, 728, F27, 12) (dual of [728, 704, 13]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {3,4,…,14}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(279, 28, F27, 9) (dual of [28, 19, 10]-code or 28-arc in PG(8,27)), using
- extended Reed–Solomon code RSe(19,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(272, 7, F27, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), 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.