Information on Result #713649
Linear OA(759, 349, F7, 23) (dual of [349, 290, 24]-code), using construction XX applied to C1 = C([36,57]), C2 = C([38,58]), C3 = C1 + C2 = C([38,57]), and C∩ = C1 ∩ C2 = C([36,58]) based on
- 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 = {36,37,…,57}, and designed minimum distance d ≥ |I|+1 = 23 [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(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 = {36,37,…,58}, and designed minimum distance d ≥ |I|+1 = 24 [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(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
- 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(759, 301, F7, 2, 23) (dual of [(301, 2), 543, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(759, 301, F7, 3, 23) (dual of [(301, 3), 844, 24]-NRT-code) | [i] | ||
| 3 | Digital (36, 59, 301)-net over F7 | [i] | ||
| 4 | Linear OOA(759, 174, F7, 2, 23) (dual of [(174, 2), 289, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(759, 116, F7, 3, 23) (dual of [(116, 3), 289, 24]-NRT-code) | [i] | ||