Information on Result #713248
Linear OA(727, 353, F7, 10) (dual of [353, 326, 11]-code), using construction XX applied to C1 = C([49,57]), C2 = C([52,58]), C3 = C1 + C2 = C([52,57]), and C∩ = C1 ∩ C2 = C([49,58]) based on
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,57}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(719, 342, F7, 7) (dual of [342, 323, 8]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {52,53,…,58}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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 = {49,50,…,58}, and designed minimum distance d ≥ |I|+1 = 11 [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 = {52,53,…,57}, and designed minimum distance d ≥ |I|+1 = 7 [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(727, 346, F7, 2, 10) (dual of [(346, 2), 665, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(727, 346, F7, 3, 10) (dual of [(346, 3), 1011, 11]-NRT-code) | [i] | ||
| 3 | Digital (17, 27, 346)-net over F7 | [i] | ||
| 4 | Linear OOA(727, 176, F7, 2, 10) (dual of [(176, 2), 325, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(727, 117, F7, 3, 10) (dual of [(117, 3), 324, 11]-NRT-code) | [i] | ||