Information on Result #693476
Linear OA(2578, 15633, F25, 27) (dual of [15633, 15555, 28]-code), using construction X applied to Ce(26) ⊂ Ce(23) based on
- linear OA(2576, 15625, F25, 27) (dual of [15625, 15549, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), 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(2595, 15699, F25, 27) (dual of [15699, 15604, 28]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2596, 15701, F25, 27) (dual of [15701, 15605, 28]-code) | [i] | ||
| 3 | Linear OOA(2578, 8559, F25, 2, 27) (dual of [(8559, 2), 17040, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (51, 78, 8559)-net over F25 | [i] | ||
| 5 | Linear OOA(2578, 7816, F25, 2, 27) (dual of [(7816, 2), 15554, 28]-NRT-code) | [i] | OOA Folding | |