Information on Result #716656
Linear OA(8153, 544, F8, 54) (dual of [544, 391, 55]-code), using construction XX applied to C1 = C([30,81]), C2 = C([28,74]), C3 = C1 + C2 = C([30,74]), and C∩ = C1 ∩ C2 = C([28,81]) based on
- linear OA(8136, 511, F8, 52) (dual of [511, 375, 53]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {30,31,…,81}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(8124, 511, F8, 47) (dual of [511, 387, 48]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {28,29,…,74}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(8142, 511, F8, 54) (dual of [511, 369, 55]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {28,29,…,81}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(8118, 511, F8, 45) (dual of [511, 393, 46]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {30,31,…,74}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(810, 26, F8, 6) (dual of [26, 16, 7]-code), using
- construction X applied to AG(F,16P) ⊂ AG(F,18P) [i] based on
- linear OA(89, 23, F8, 6) (dual of [23, 14, 7]-code), using algebraic-geometric code AG(F,16P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- linear OA(87, 23, F8, 4) (dual of [23, 16, 5]-code), using algebraic-geometric code AG(F,18P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(89, 23, F8, 6) (dual of [23, 14, 7]-code), using algebraic-geometric code AG(F,16P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- construction X applied to AG(F,16P) ⊂ AG(F,18P) [i] based on
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), 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.