Information on Result #675302
Linear OA(3227, 6566, F3, 42) (dual of [6566, 6339, 43]-code), using construction X applied to C([0,21]) ⊂ C([0,19]) based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3209, 6562, F3, 39) (dual of [6562, 6353, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (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(3227, 3875, F3, 2, 42) (dual of [(3875, 2), 7523, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3227, 3875, F3, 3, 42) (dual of [(3875, 3), 11398, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(3227, 3875, F3, 4, 42) (dual of [(3875, 4), 15273, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3227, 3875, F3, 5, 42) (dual of [(3875, 5), 19148, 43]-NRT-code) | [i] | ||
| 5 | Digital (185, 227, 3875)-net over F3 | [i] | ||