Information on Result #2273890
Linear OA(4259, 16411, F4, 49) (dual of [16411, 16152, 50]-code), using 1 times code embedding in larger space based on linear OA(4258, 16410, F4, 49) (dual of [16410, 16152, 50]-code), using
- construction X applied to Ce(48) ⊂ Ce(44) [i] based on
- linear OA(4253, 16384, F4, 49) (dual of [16384, 16131, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-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(4259, 12319, F4, 2, 49) (dual of [(12319, 2), 24379, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4259, 12319, F4, 3, 49) (dual of [(12319, 3), 36698, 50]-NRT-code) | [i] | ||
| 3 | Digital (210, 259, 12319)-net over F4 | [i] | ||