Information on Result #694145
Linear OA(2538, 636, F25, 18) (dual of [636, 598, 19]-code), using construction X applied to Ce(17) ⊂ Ce(13) based on
- linear OA(2535, 625, F25, 18) (dual of [625, 590, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2527, 625, F25, 14) (dual of [625, 598, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-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(2538, 477, F25, 2, 18) (dual of [(477, 2), 916, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (20, 38, 477)-net over F25 | [i] | ||
| 3 | Linear OOA(2538, 318, F25, 2, 18) (dual of [(318, 2), 598, 19]-NRT-code) | [i] | OOA Folding | |