Information on Result #675752
Linear OA(3227, 2192, F3, 48) (dual of [2192, 1965, 49]-code), using construction X applied to C([0,24]) ⊂ C([0,22]) based on
- linear OA(3225, 2188, F3, 49) (dual of [2188, 1963, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(3211, 2188, F3, 45) (dual of [2188, 1977, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (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, 1945, F3, 2, 48) (dual of [(1945, 2), 3663, 49]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3227, 1945, F3, 3, 48) (dual of [(1945, 3), 5608, 49]-NRT-code) | [i] | ||
| 3 | Linear OOA(3227, 1945, F3, 4, 48) (dual of [(1945, 4), 7553, 49]-NRT-code) | [i] | ||
| 4 | Linear OOA(3227, 1945, F3, 5, 48) (dual of [(1945, 5), 9498, 49]-NRT-code) | [i] | ||
| 5 | Digital (179, 227, 1945)-net over F3 | [i] | ||