Information on Result #952843
Linear OOA(3140, 59059, F3, 3, 19) (dual of [(59059, 3), 177037, 20]-NRT-code), using OOA 3-folding based on linear OA(3140, 177177, F3, 19) (dual of [177177, 177037, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3139, 177176, F3, 19) (dual of [177176, 177037, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(3111, 177148, F3, 15) (dual of [177148, 177037, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
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(3140, 59059, F3, 4, 19) (dual of [(59059, 4), 236096, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3140, 59059, F3, 5, 19) (dual of [(59059, 5), 295155, 20]-NRT-code) | [i] | ||
| 3 | Digital (121, 140, 59059)-net over F3 | [i] | ||