Information on Result #682583
Linear OA(586, 15639, F5, 17) (dual of [15639, 15553, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(585, 15626, F5, 17) (dual of [15626, 15541, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(573, 15626, F5, 15) (dual of [15626, 15553, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(586, 14663, F5, 2, 17) (dual of [(14663, 2), 29240, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(586, 14663, F5, 3, 17) (dual of [(14663, 3), 43903, 18]-NRT-code) | [i] | ||
| 3 | Digital (69, 86, 14663)-net over F5 | [i] | ||