Information on Result #1323601
Linear OA(4255, 65599, F4, 41) (dual of [65599, 65344, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(414, 62, F4, 7) (dual of [62, 48, 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(4256, 65600, F4, 41) (dual of [65600, 65344, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4258, 65603, F4, 41) (dual of [65603, 65345, 42]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OA(4259, 65605, F4, 41) (dual of [65605, 65346, 42]-code) | [i] | ||
| 4 | Linear OA(4260, 65607, F4, 41) (dual of [65607, 65347, 42]-code) | [i] | ||
| 5 | Linear OOA(4255, 32799, F4, 2, 41) (dual of [(32799, 2), 65343, 42]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4255, 21866, F4, 3, 41) (dual of [(21866, 3), 65343, 42]-NRT-code) | [i] | ||