Information on Result #715398
Linear OA(882, 545, F8, 27) (dual of [545, 463, 28]-code), using construction XX applied to C1 = C([503,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([503,18]) based on
- linear OA(864, 511, F8, 25) (dual of [511, 447, 26]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,16}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(849, 511, F8, 19) (dual of [511, 462, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,18}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(843, 511, F8, 17) (dual of [511, 468, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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.