Information on Result #2266441
Linear OA(3212, 19733, F3, 33) (dual of [19733, 19521, 34]-code), using 2 times code embedding in larger space based on linear OA(3210, 19731, F3, 33) (dual of [19731, 19521, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(3199, 19684, F3, 33) (dual of [19684, 19485, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3163, 19684, F3, 27) (dual of [19684, 19521, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(311, 47, F3, 5) (dual of [47, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-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(3212, 10948, F3, 2, 33) (dual of [(10948, 2), 21684, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3212, 10948, F3, 3, 33) (dual of [(10948, 3), 32632, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3212, 10948, F3, 4, 33) (dual of [(10948, 4), 43580, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3212, 10948, F3, 5, 33) (dual of [(10948, 5), 54528, 34]-NRT-code) | [i] | ||
| 5 | Digital (179, 212, 10948)-net over F3 | [i] | ||