Information on Result #726731
Linear OA(27103, 786, F27, 43) (dual of [786, 683, 44]-code), using construction XX applied to C1 = C([723,27]), C2 = C([7,37]), C3 = C1 + C2 = C([7,27]), and C∩ = C1 ∩ C2 = C([723,37]) based on
- linear OA(2763, 728, F27, 33) (dual of [728, 665, 34]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−5,−4,…,27}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2761, 728, F27, 31) (dual of [728, 667, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {7,8,…,37}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- 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 = {−5,−4,…,37}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2742, 728, F27, 21) (dual of [728, 686, 22]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {7,8,…,27}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2712, 30, F27, 11) (dual of [30, 18, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2712, 38, F27, 11) (dual of [38, 26, 12]-code), using
- extended algebraic-geometric code AGe(F,26P) [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(2712, 38, F27, 11) (dual of [38, 26, 12]-code), using
- 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]
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.