Information on Result #2255409
Linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using 1 times truncation based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(2599, 355362, F25, 2, 25) (dual of [(355362, 2), 710625, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (74, 99, 355362)-net over F25 | [i] | ||
| 3 | Linear OOA(2599, 195319, F25, 2, 25) (dual of [(195319, 2), 390539, 26]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2599, 32553, F25, 25, 25) (dual of [(32553, 25), 813726, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |