Information on Result #712637
Linear OA(712, 174, F7, 5) (dual of [174, 162, 6]-code), using construction X applied to C([24,28]) ⊂ C([25,28]) based on
- linear OA(712, 171, F7, 5) (dual of [171, 159, 6]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {24,25,26,27,28}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(79, 171, F7, 4) (dual of [171, 162, 5]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {25,26,27,28}, and designed minimum distance d ≥ |I|+1 = 5 [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(712, 174, F7, 2, 5) (dual of [(174, 2), 336, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(712, 174, F7, 3, 5) (dual of [(174, 3), 510, 6]-NRT-code) | [i] | ||
| 3 | Digital (7, 12, 174)-net over F7 | [i] | ||
| 4 | Linear OOA(712, 87, F7, 2, 5) (dual of [(87, 2), 162, 6]-NRT-code) | [i] | OOA Folding | |