Information on Result #678085
Linear OA(4187, 1048623, F4, 23) (dual of [1048623, 1048436, 24]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) based on
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4141, 1048577, F4, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(46, 46, F4, 3) (dual of [46, 40, 4]-code or 46-cap in PG(5,4)), using
- discarding factors / shortening the dual code based on linear OA(46, 102, F4, 3) (dual of [102, 96, 4]-code or 102-cap in PG(5,4)), 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(4187, 622144, F4, 2, 23) (dual of [(622144, 2), 1244101, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4187, 622144, F4, 3, 23) (dual of [(622144, 3), 1866245, 24]-NRT-code) | [i] | ||
| 3 | Digital (164, 187, 622144)-net over F4 | [i] | ||