Information on Result #2277192
Linear OA(563, 3138, F5, 15) (dual of [3138, 3075, 16]-code), using 1 times code embedding in larger space based on linear OA(562, 3137, F5, 15) (dual of [3137, 3075, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(561, 3126, F5, 15) (dual of [3126, 3065, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(551, 3126, F5, 13) (dual of [3126, 3075, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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(563, 3046, F5, 2, 15) (dual of [(3046, 2), 6029, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(563, 3046, F5, 3, 15) (dual of [(3046, 3), 9075, 16]-NRT-code) | [i] | ||
| 3 | Digital (48, 63, 3046)-net over F5 | [i] | ||
| 4 | Linear OOA(563, 1569, F5, 2, 15) (dual of [(1569, 2), 3075, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(563, 1046, F5, 3, 15) (dual of [(1046, 3), 3075, 16]-NRT-code) | [i] | ||