Information on Result #675374
Linear OA(3194, 6596, F3, 33) (dual of [6596, 6402, 34]-code), using construction X4 applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(333, 34, F3, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,3)), using
- dual of repetition code with length 34 [i]
- linear OA(31, 34, F3, 1) (dual of [34, 33, 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(3194, 5771, F3, 2, 33) (dual of [(5771, 2), 11348, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3194, 5771, F3, 3, 33) (dual of [(5771, 3), 17119, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3194, 5771, F3, 4, 33) (dual of [(5771, 4), 22890, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3194, 5771, F3, 5, 33) (dual of [(5771, 5), 28661, 34]-NRT-code) | [i] | ||
| 5 | Digital (161, 194, 5771)-net over F3 | [i] | ||