Information on Result #693212
Linear OA(2556, 390644, F25, 14) (dual of [390644, 390588, 15]-code), using construction X applied to Ce(13) ⊂ Ce(9) based on
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(2556, 390644, F25, 2, 14) (dual of [(390644, 2), 781232, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (42, 56, 390644)-net over F25 | [i] | ||
| 3 | Linear OOA(2556, 195322, F25, 2, 14) (dual of [(195322, 2), 390588, 15]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2556, 55806, F25, 14, 14) (dual of [(55806, 14), 781228, 15]-NRT-code) | [i] | OA Folding and Stacking | |