Information on Result #678573
Linear OA(4198, 65574, F4, 31) (dual of [65574, 65376, 32]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- 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(4161, 65537, F4, 27) (dual of [65537, 65376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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(4198, 47824, F4, 2, 31) (dual of [(47824, 2), 95450, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4198, 47824, F4, 3, 31) (dual of [(47824, 3), 143274, 32]-NRT-code) | [i] | ||
| 3 | Digital (167, 198, 47824)-net over F4 | [i] | ||