Information on Result #726432
Linear OA(2786, 768, F27, 38) (dual of [768, 682, 39]-code), using construction XX applied to C1 = C([722,27]), C2 = C([5,31]), C3 = C1 + C2 = C([5,27]), and C∩ = C1 ∩ C2 = C([722,31]) based on
- linear OA(2765, 728, F27, 34) (dual of [728, 663, 35]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−6,−5,…,27}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2753, 728, F27, 27) (dual of [728, 675, 28]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {5,6,…,31}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2772, 728, F27, 38) (dual of [728, 656, 39]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−6,−5,…,31}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2746, 728, F27, 23) (dual of [728, 682, 24]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {5,6,…,27}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2711, 30, F27, 10) (dual of [30, 19, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2711, 38, F27, 10) (dual of [38, 27, 11]-code), using
- extended algebraic-geometric code AGe(F,27P) [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- discarding factors / shortening the dual code based on linear OA(2711, 38, F27, 10) (dual of [38, 27, 11]-code), using
- linear OA(273, 10, F27, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,27) or 10-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
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.