Information on Result #715820
Linear OA(8109, 545, F8, 37) (dual of [545, 436, 38]-code), using construction XX applied to C1 = C([503,26]), C2 = C([0,28]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([503,28]) based on
- linear OA(891, 511, F8, 35) (dual of [511, 420, 36]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,26}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(876, 511, F8, 29) (dual of [511, 435, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(897, 511, F8, 37) (dual of [511, 414, 38]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,28}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(811, 27, F8, 7) (dual of [27, 16, 8]-code), using
- construction X applied to AG(F,8P) ⊂ AG(F,9P) [i] based on
- linear OA(810, 24, F8, 7) (dual of [24, 14, 8]-code), using algebraic-geometric code AG(F,8P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F8 [i]
- linear OA(88, 24, F8, 5) (dual of [24, 16, 6]-code), using algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [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
- construction X applied to AG(F,8P) ⊂ AG(F,9P) [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.