Information on Result #2255397
Linear OA(2575, 15636, F25, 25) (dual of [15636, 15561, 26]-code), using 1 times truncation based on linear OA(2576, 15637, F25, 26) (dual of [15637, 15561, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(253, 12, F25, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,25) or 12-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(2591, 15702, F25, 25) (dual of [15702, 15611, 26]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2592, 15704, F25, 25) (dual of [15704, 15612, 26]-code) | [i] | ||
| 3 | Linear OOA(2575, 12347, F25, 2, 25) (dual of [(12347, 2), 24619, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (50, 75, 12347)-net over F25 | [i] | ||
| 5 | Linear OOA(2575, 7818, F25, 2, 25) (dual of [(7818, 2), 15561, 26]-NRT-code) | [i] | OOA Folding | |