Information on Result #713653
Linear OA(763, 353, F7, 24) (dual of [353, 290, 25]-code), using construction XX applied to C1 = C([35,57]), C2 = C([38,58]), C3 = C1 + C2 = C([38,57]), and C∩ = C1 ∩ C2 = C([35,58]) based on
- 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 = {35,36,…,57}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(755, 342, F7, 21) (dual of [342, 287, 22]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {38,39,…,58}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(761, 342, F7, 24) (dual of [342, 281, 25]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {35,36,…,58}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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 = {38,39,…,57}, and designed minimum distance d ≥ |I|+1 = 21 [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(763, 351, F7, 2, 24) (dual of [(351, 2), 639, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(763, 351, F7, 3, 24) (dual of [(351, 3), 990, 25]-NRT-code) | [i] | ||
| 3 | Digital (39, 63, 351)-net over F7 | [i] | ||
| 4 | Linear OOA(763, 176, F7, 2, 24) (dual of [(176, 2), 289, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(763, 117, F7, 3, 24) (dual of [(117, 3), 288, 25]-NRT-code) | [i] | ||