Information on Result #675831
Linear OA(3175, 2222, F3, 35) (dual of [2222, 2047, 36]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) 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(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(36, 34, F3, 3) (dual of [34, 28, 4]-code or 34-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
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(3175, 2127, F3, 2, 35) (dual of [(2127, 2), 4079, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3175, 2127, F3, 3, 35) (dual of [(2127, 3), 6206, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(3175, 2127, F3, 4, 35) (dual of [(2127, 4), 8333, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3175, 2127, F3, 5, 35) (dual of [(2127, 5), 10460, 36]-NRT-code) | [i] | ||
| 5 | Digital (140, 175, 2127)-net over F3 | [i] | ||