Information on Result #2244496
Linear OA(4215, 16409, F4, 40) (dual of [16409, 16194, 41]-code), using 1 times truncation based on linear OA(4216, 16410, F4, 41) (dual of [16410, 16194, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(4215, 12279, F4, 2, 40) (dual of [(12279, 2), 24343, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4215, 12279, F4, 3, 40) (dual of [(12279, 3), 36622, 41]-NRT-code) | [i] | ||
| 3 | Digital (175, 215, 12279)-net over F4 | [i] | ||
| 4 | Linear OOA(4215, 8204, F4, 2, 40) (dual of [(8204, 2), 16193, 41]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4215, 5469, F4, 3, 40) (dual of [(5469, 3), 16192, 41]-NRT-code) | [i] | ||