Information on Result #693328
Linear OA(2576, 15641, F25, 25) (dual of [15641, 15565, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2561, 15626, F25, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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 OA(2592, 15707, F25, 25) (dual of [15707, 15615, 26]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(2576, 14204, F25, 2, 25) (dual of [(14204, 2), 28332, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (51, 76, 14204)-net over F25 | [i] | ||
| 4 | Linear OOA(2576, 7820, F25, 2, 25) (dual of [(7820, 2), 15564, 26]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2576, 1303, F25, 25, 25) (dual of [(1303, 25), 32499, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |