Information on Result #2284113
Linear OA(979, 13127, F9, 20) (dual of [13127, 13048, 21]-code), using 1 times code embedding in larger space based on linear OA(978, 13126, F9, 20) (dual of [13126, 13048, 21]-code), using
- trace code [i] based on linear OA(8139, 6563, F81, 20) (dual of [6563, 6524, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
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(979, 12875, F9, 2, 20) (dual of [(12875, 2), 25671, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(979, 12875, F9, 3, 20) (dual of [(12875, 3), 38546, 21]-NRT-code) | [i] | ||
| 3 | Digital (59, 79, 12875)-net over F9 | [i] | ||