Information on Result #713474
Linear OA(770, 377, F7, 23) (dual of [377, 307, 24]-code), using construction XX applied to C1 = C([335,12]), C2 = C([0,15]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([335,15]) based on
- linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−7,−6,…,12}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(758, 342, F7, 23) (dual of [342, 284, 24]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−7,−6,…,15}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(734, 342, F7, 13) (dual of [342, 308, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(710, 27, F7, 6) (dual of [27, 17, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(710, 25, F7, 6) (dual of [25, 15, 7]-code), using an extension Ce(5) of the narrow-sense BCH-code C(I) with length 24 | 72−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(78, 25, F7, 5) (dual of [25, 17, 6]-code), using an extension Ce(4) of the narrow-sense BCH-code C(I) with length 24 | 72−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 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
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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]
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.