Information on Result #675787
Linear OA(387, 2192, F3, 18) (dual of [2192, 2105, 19]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(385, 2188, F3, 19) (dual of [2188, 2103, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(371, 2188, F3, 15) (dual of [2188, 2117, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(387, 1233, F3, 2, 18) (dual of [(1233, 2), 2379, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(387, 1233, F3, 3, 18) (dual of [(1233, 3), 3612, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(387, 1233, F3, 4, 18) (dual of [(1233, 4), 4845, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(387, 1233, F3, 5, 18) (dual of [(1233, 5), 6078, 19]-NRT-code) | [i] | ||
| 5 | Digital (69, 87, 1233)-net over F3 | [i] | ||