Information on Result #675748
Linear OA(3226, 2203, F3, 47) (dual of [2203, 1977, 48]-code), using construction X applied to C([0,24]) ⊂ C([0,22]) 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(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3226, 2100, F3, 2, 47) (dual of [(2100, 2), 3974, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3226, 2100, F3, 3, 47) (dual of [(2100, 3), 6074, 48]-NRT-code) | [i] | ||
| 3 | Linear OOA(3226, 2100, F3, 4, 47) (dual of [(2100, 4), 8174, 48]-NRT-code) | [i] | ||
| 4 | Linear OOA(3226, 2100, F3, 5, 47) (dual of [(2100, 5), 10274, 48]-NRT-code) | [i] | ||
| 5 | Digital (179, 226, 2100)-net over F3 | [i] | ||