Information on Result #675762
Linear OA(3170, 2203, F3, 35) (dual of [2203, 2033, 36]-code), using construction X applied to C([0,18]) ⊂ C([0,16]) based on
- linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3155, 2188, F3, 33) (dual of [2188, 2033, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(3170, 1796, F3, 2, 35) (dual of [(1796, 2), 3422, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3170, 1796, F3, 3, 35) (dual of [(1796, 3), 5218, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(3170, 1796, F3, 4, 35) (dual of [(1796, 4), 7014, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3170, 1796, F3, 5, 35) (dual of [(1796, 5), 8810, 36]-NRT-code) | [i] | ||
| 5 | Digital (135, 170, 1796)-net over F3 | [i] | ||