Information on Result #726330
Linear OA(2789, 781, F27, 37) (dual of [781, 692, 38]-code), using construction XX applied to C1 = C([0,27]), C2 = C([12,36]), C3 = C1 + C2 = C([12,27]), and C∩ = C1 ∩ C2 = C([0,36]) based on
- linear OA(2753, 728, F27, 28) (dual of [728, 675, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {12,13,…,36}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2770, 728, F27, 37) (dual of [728, 658, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2732, 728, F27, 16) (dual of [728, 696, 17]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {12,13,…,27}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2711, 28, F27, 11) (dual of [28, 17, 12]-code or 28-arc in PG(10,27)), using
- extended Reed–Solomon code RSe(17,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(278, 25, F27, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,27)), using
- discarding factors / shortening the dual code based on linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)), using
- Reed–Solomon code RS(19,27) [i]
- discarding factors / shortening the dual code based on linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)), 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.