Information on Result #693335
Linear OA(2534, 15641, F25, 11) (dual of [15641, 15607, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- linear OA(2531, 15626, F25, 11) (dual of [15626, 15595, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2519, 15626, F25, 7) (dual of [15626, 15607, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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(2534, 15641, F25, 2, 11) (dual of [(15641, 2), 31248, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 34, 15641)-net over F25 | [i] | ||
| 3 | Linear OOA(2534, 7820, F25, 2, 11) (dual of [(7820, 2), 15606, 12]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2534, 3128, F25, 11, 11) (dual of [(3128, 11), 34374, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |