Information on Result #2267218
Linear OA(3231, 2208, F3, 49) (dual of [2208, 1977, 50]-code), using 1 times code embedding in larger space based on linear OA(3230, 2207, F3, 49) (dual of [2207, 1977, 50]-code), using
- construction X applied to C([0,24]) ⊂ C([0,22]) [i] based on
- linear OA(3225, 2188, F3, 49) (dual of [2188, 1963, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(3211, 2188, F3, 45) (dual of [2188, 1977, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(35, 19, F3, 3) (dual of [19, 14, 4]-code or 19-cap in PG(4,3)), 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(3231, 1942, F3, 2, 49) (dual of [(1942, 2), 3653, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3231, 1942, F3, 3, 49) (dual of [(1942, 3), 5595, 50]-NRT-code) | [i] | ||
| 3 | Linear OOA(3231, 1942, F3, 4, 49) (dual of [(1942, 4), 7537, 50]-NRT-code) | [i] | ||
| 4 | Linear OOA(3231, 1942, F3, 5, 49) (dual of [(1942, 5), 9479, 50]-NRT-code) | [i] | ||
| 5 | Digital (182, 231, 1942)-net over F3 | [i] | ||
| 6 | Linear OOA(3231, 1104, F3, 2, 49) (dual of [(1104, 2), 1977, 50]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3231, 736, F3, 3, 49) (dual of [(736, 3), 1977, 50]-NRT-code) | [i] | ||
| 8 | Linear OOA(3231, 552, F3, 4, 49) (dual of [(552, 4), 1977, 50]-NRT-code) | [i] | ||