Information on Result #2266188
Linear OA(3189, 19745, F3, 29) (dual of [19745, 19556, 30]-code), using 2 times code embedding in larger space based on linear OA(3187, 19743, F3, 29) (dual of [19743, 19556, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), 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(3189, 11444, F3, 2, 29) (dual of [(11444, 2), 22699, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3189, 11444, F3, 3, 29) (dual of [(11444, 3), 34143, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3189, 11444, F3, 4, 29) (dual of [(11444, 4), 45587, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3189, 11444, F3, 5, 29) (dual of [(11444, 5), 57031, 30]-NRT-code) | [i] | ||
| 5 | Digital (160, 189, 11444)-net over F3 | [i] | ||
| 6 | Linear OOA(3189, 3949, F3, 5, 29) (dual of [(3949, 5), 19556, 30]-NRT-code) | [i] | OOA Folding | |