Information on Result #1530987
Linear OOA(3228, 1808, F3, 3, 49) (dual of [(1808, 3), 5196, 50]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3228, 1808, F3, 49) (dual of [1808, 1580, 50]-code), using
- discarding factors / shortening the dual code based on linear OA(3228, 2192, F3, 49) (dual of [2192, 1964, 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(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
- dual of repetition code with length 4 [i]
- oval in PG(2, 3) [i]
- construction X applied to C([0,24]) ⊂ C([0,22]) [i] based on
Mode: 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, 904, F3, 5, 49) (dual of [(904, 5), 4292, 50]-NRT-code) | [i] | OOA Folding | |