Information on Result #712934
Linear OA(784, 182, F7, 37) (dual of [182, 98, 38]-code), using construction XX applied to C1 = C([168,32]), C2 = C([0,33]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([168,33]) based on
- linear OA(779, 171, F7, 36) (dual of [171, 92, 37]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,32}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(776, 171, F7, 34) (dual of [171, 95, 35]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(782, 171, F7, 37) (dual of [171, 89, 38]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,33}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(773, 171, F7, 33) (dual of [171, 98, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(784, 91, F7, 2, 37) (dual of [(91, 2), 98, 38]-NRT-code) | [i] | OOA Folding | |