Information on Result #713911
Linear OA(782, 354, F7, 31) (dual of [354, 272, 32]-code), using construction XX applied to C1 = C([340,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([340,28]) based on
- linear OA(776, 342, F7, 29) (dual of [342, 266, 30]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(772, 342, F7, 28) (dual of [342, 270, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(779, 342, F7, 31) (dual of [342, 263, 32]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(769, 342, F7, 26) (dual of [342, 273, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
- linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 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.