Information on Result #2272939
Linear OA(4175, 16411, F4, 33) (dual of [16411, 16236, 34]-code), using 1 times code embedding in larger space based on linear OA(4174, 16410, F4, 33) (dual of [16410, 16236, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(4175, 9889, F4, 2, 33) (dual of [(9889, 2), 19603, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4175, 9889, F4, 3, 33) (dual of [(9889, 3), 29492, 34]-NRT-code) | [i] | ||
| 3 | Digital (142, 175, 9889)-net over F4 | [i] | ||