Information on Result #678582
Linear OA(4134, 65574, F4, 21) (dual of [65574, 65440, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(4129, 65537, F4, 21) (dual of [65537, 65408, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(45, 37, F4, 3) (dual of [37, 32, 4]-code or 37-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(4134, 43288, F4, 2, 21) (dual of [(43288, 2), 86442, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4134, 43288, F4, 3, 21) (dual of [(43288, 3), 129730, 22]-NRT-code) | [i] | ||
| 3 | Digital (113, 134, 43288)-net over F4 | [i] | ||