Information on Result #679126
Linear OA(4160, 16410, F4, 30) (dual of [16410, 16250, 31]-code), using construction X applied to Ce(29) ⊂ Ce(25) based on
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(4160, 9857, F4, 2, 30) (dual of [(9857, 2), 19554, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4160, 9857, F4, 3, 30) (dual of [(9857, 3), 29411, 31]-NRT-code) | [i] | ||
| 3 | Digital (130, 160, 9857)-net over F4 | [i] | ||
| 4 | Linear OOA(4160, 8205, F4, 2, 30) (dual of [(8205, 2), 16250, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4160, 5470, F4, 3, 30) (dual of [(5470, 3), 16250, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(4160, 1094, F4, 30, 30) (dual of [(1094, 30), 32660, 31]-NRT-code) | [i] | OA Folding and Stacking | |