Information on Result #2265858
Linear OA(3158, 19733, F3, 24) (dual of [19733, 19575, 25]-code), using 4 times code embedding in larger space based on linear OA(3154, 19729, F3, 24) (dual of [19729, 19575, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-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(3158, 11480, F3, 2, 24) (dual of [(11480, 2), 22802, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3158, 11480, F3, 3, 24) (dual of [(11480, 3), 34282, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3158, 11480, F3, 4, 24) (dual of [(11480, 4), 45762, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(3158, 11480, F3, 5, 24) (dual of [(11480, 5), 57242, 25]-NRT-code) | [i] | ||
| 5 | Digital (134, 158, 11480)-net over F3 | [i] | ||