Information on Result #813450
Linear OOA(3115, 9858, F3, 2, 18) (dual of [(9858, 2), 19601, 19]-NRT-code), using OOA 2-folding based on linear OA(3115, 19716, F3, 18) (dual of [19716, 19601, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(382, 19683, F3, 14) (dual of [19683, 19601, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3115, 9858, F3, 3, 18) (dual of [(9858, 3), 29459, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3115, 9858, F3, 4, 18) (dual of [(9858, 4), 39317, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3115, 9858, F3, 5, 18) (dual of [(9858, 5), 49175, 19]-NRT-code) | [i] | ||
| 4 | Digital (97, 115, 9858)-net over F3 | [i] | ||