Information on Result #730099
Linear OA(819, 166, F81, 6) (dual of [166, 157, 7]-code), using construction X applied to C([38,43]) ⊂ C([39,43]) based on
- linear OA(819, 164, F81, 6) (dual of [164, 155, 7]-code), using the BCH-code C(I) with length 164 | 812−1, defining interval I = {38,39,…,43}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(817, 164, F81, 5) (dual of [164, 157, 6]-code), using the BCH-code C(I) with length 164 | 812−1, defining interval I = {39,40,41,42,43}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 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 OA(8134, 6729, F81, 13) (dual of [6729, 6695, 14]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(8146, 531610, F81, 13) (dual of [531610, 531564, 14]-code) | [i] | ||
| 3 | Linear OA(8132, 6729, F81, 12) (dual of [6729, 6697, 13]-code) | [i] | ||
| 4 | Linear OA(8143, 531610, F81, 12) (dual of [531610, 531567, 13]-code) | [i] | ||
| 5 | Linear OOA(819, 166, F81, 2, 6) (dual of [(166, 2), 323, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(819, 166, F81, 3, 6) (dual of [(166, 3), 489, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(819, 166, F81, 4, 6) (dual of [(166, 4), 655, 7]-NRT-code) | [i] | ||
| 8 | Digital (3, 9, 166)-net over F81 | [i] | ||
| 9 | Linear OA(8110, 226, F81, 6) (dual of [226, 216, 7]-code) | [i] | Varšamov–Edel Lengthening | |