Information on Result #1323679
Linear OA(4225, 16441, F4, 41) (dual of [16441, 16216, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) 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(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
Mode: 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 OA(4226, 16442, F4, 41) (dual of [16442, 16216, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4227, 16444, F4, 41) (dual of [16444, 16217, 42]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OA(4228, 16446, F4, 41) (dual of [16446, 16218, 42]-code) | [i] | ||
| 4 | Linear OA(4229, 16448, F4, 41) (dual of [16448, 16219, 42]-code) | [i] | ||
| 5 | Linear OOA(4225, 8220, F4, 2, 41) (dual of [(8220, 2), 16215, 42]-NRT-code) | [i] | OOA Folding | |