Information on Result #678935
Linear OA(4258, 16418, F4, 47) (dual of [16418, 16160, 48]-code), using construction X applied to C([0,24]) ⊂ C([0,21]) based on
- linear OA(4253, 16385, F4, 49) (dual of [16385, 16132, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(4225, 16385, F4, 43) (dual of [16385, 16160, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(45, 33, F4, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4258, 16088, F4, 2, 47) (dual of [(16088, 2), 31918, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4258, 16088, F4, 3, 47) (dual of [(16088, 3), 48006, 48]-NRT-code) | [i] | ||
| 3 | Digital (211, 258, 16088)-net over F4 | [i] | ||