Information on Result #815002
Linear OOA(3187, 9858, F3, 2, 30) (dual of [(9858, 2), 19529, 31]-NRT-code), using OOA 2-folding based on linear OA(3187, 19716, F3, 30) (dual of [19716, 19529, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(3187, 9858, F3, 3, 30) (dual of [(9858, 3), 29387, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3187, 9858, F3, 4, 30) (dual of [(9858, 4), 39245, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3187, 9858, F3, 5, 30) (dual of [(9858, 5), 49103, 31]-NRT-code) | [i] | ||
| 4 | Digital (157, 187, 9858)-net over F3 | [i] | ||