Information on Result #675040
Linear OA(3223, 19726, F3, 35) (dual of [19726, 19503, 36]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3217, 19684, F3, 37) (dual of [19684, 19467, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 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(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(3223, 10635, F3, 2, 35) (dual of [(10635, 2), 21047, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3223, 10635, F3, 3, 35) (dual of [(10635, 3), 31682, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(3223, 10635, F3, 4, 35) (dual of [(10635, 4), 42317, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3223, 10635, F3, 5, 35) (dual of [(10635, 5), 52952, 36]-NRT-code) | [i] | ||
| 5 | Digital (188, 223, 10635)-net over F3 | [i] | ||