Information on Result #713184
Linear OA(718, 353, F7, 6) (dual of [353, 335, 7]-code), using construction XX applied to C1 = C([339,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([339,2]) based on
- linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−3,−2,−1,0,1}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(716, 342, F7, 6) (dual of [342, 326, 7]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−3,−2,…,2}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(74, 342, F7, 2) (dual of [342, 338, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [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.