Information on Result #678892
Linear OA(4256, 16402, F4, 48) (dual of [16402, 16146, 49]-code), using construction X applied to C([0,24]) ⊂ C([0,22]) 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(4239, 16385, F4, 45) (dual of [16385, 16146, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(43, 17, F4, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), 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(4256, 13013, F4, 2, 48) (dual of [(13013, 2), 25770, 49]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4256, 13013, F4, 3, 48) (dual of [(13013, 3), 38783, 49]-NRT-code) | [i] | ||
| 3 | Digital (208, 256, 13013)-net over F4 | [i] | ||