Information on Result #675311
Linear OA(3195, 6566, F3, 36) (dual of [6566, 6371, 37]-code), using construction X applied to C([0,18]) ⊂ C([0,16]) 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(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
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(3195, 3539, F3, 2, 36) (dual of [(3539, 2), 6883, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3195, 3539, F3, 3, 36) (dual of [(3539, 3), 10422, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3195, 3539, F3, 4, 36) (dual of [(3539, 4), 13961, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3195, 3539, F3, 5, 36) (dual of [(3539, 5), 17500, 37]-NRT-code) | [i] | ||
| 5 | Digital (159, 195, 3539)-net over F3 | [i] | ||