Information on Result #693075
Linear OA(2568, 390645, F25, 17) (dual of [390645, 390577, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
- linear OA(2565, 390626, F25, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2549, 390626, F25, 13) (dual of [390626, 390577, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-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(2568, 390645, F25, 2, 17) (dual of [(390645, 2), 781222, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (51, 68, 390645)-net over F25 | [i] | ||
| 3 | Linear OOA(2568, 195322, F25, 2, 17) (dual of [(195322, 2), 390576, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2568, 48830, F25, 17, 17) (dual of [(48830, 17), 830042, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |