Information on Result #713582
Linear OA(758, 354, F7, 22) (dual of [354, 296, 23]-code), using construction XX applied to C1 = C([45,64]), C2 = C([43,61]), C3 = C1 + C2 = C([45,61]), and C∩ = C1 ∩ C2 = C([43,64]) 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 = {45,46,…,64}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {43,44,…,61}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(755, 342, F7, 22) (dual of [342, 287, 23]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {43,44,…,64}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(746, 342, F7, 17) (dual of [342, 296, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {45,46,…,61}, and designed minimum distance d ≥ |I|+1 = 18 [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(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), 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(758, 344, F7, 2, 22) (dual of [(344, 2), 630, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(758, 344, F7, 3, 22) (dual of [(344, 3), 974, 23]-NRT-code) | [i] | ||
| 3 | Digital (36, 58, 344)-net over F7 | [i] | ||
| 4 | Linear OOA(758, 177, F7, 2, 22) (dual of [(177, 2), 296, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(758, 118, F7, 3, 22) (dual of [(118, 3), 296, 23]-NRT-code) | [i] | ||