Information on Result #675054
Linear OA(3187, 19726, F3, 29) (dual of [19726, 19539, 30]-code), using construction X applied to C([0,15]) ⊂ C([0,12]) based on
- linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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, 10548, F3, 2, 29) (dual of [(10548, 2), 20909, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3187, 10548, F3, 3, 29) (dual of [(10548, 3), 31457, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3187, 10548, F3, 4, 29) (dual of [(10548, 4), 42005, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3187, 10548, F3, 5, 29) (dual of [(10548, 5), 52553, 30]-NRT-code) | [i] | ||
| 5 | Digital (158, 187, 10548)-net over F3 | [i] | ||