Information on Result #713271
Linear OA(730, 353, F7, 11) (dual of [353, 323, 12]-code), using construction XX applied to C1 = C([340,7]), C2 = C([1,8]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([340,8]) based on
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,7}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(721, 342, F7, 8) (dual of [342, 321, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(718, 342, F7, 7) (dual of [342, 324, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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.