Information on Result #954250
Linear OOA(3228, 59059, F3, 3, 31) (dual of [(59059, 3), 176949, 32]-NRT-code), using OOA 3-folding based on linear OA(3228, 177177, F3, 31) (dual of [177177, 176949, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3227, 177176, F3, 31) (dual of [177176, 176949, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(3221, 177148, F3, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3199, 177148, F3, 27) (dual of [177148, 176949, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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([0,15]) ⊂ C([0,13]) [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(3228, 51662, F3, 4, 31) (dual of [(51662, 4), 206420, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3228, 51662, F3, 5, 31) (dual of [(51662, 5), 258082, 32]-NRT-code) | [i] | ||
| 3 | Digital (197, 228, 51662)-net over F3 | [i] | ||