Information on Result #678900
Linear OA(4214, 16402, F4, 40) (dual of [16402, 16188, 41]-code), using construction X applied to C([0,20]) ⊂ C([0,18]) based on
- linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4197, 16385, F4, 37) (dual of [16385, 16188, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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(4214, 11838, F4, 2, 40) (dual of [(11838, 2), 23462, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4214, 11838, F4, 3, 40) (dual of [(11838, 3), 35300, 41]-NRT-code) | [i] | ||
| 3 | Digital (174, 214, 11838)-net over F4 | [i] | ||