Information on Result #693531
Linear OA(2588, 15640, F25, 30) (dual of [15640, 15552, 31]-code), using construction X applied to Ce(29) ⊂ Ce(25) based on
- linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(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 OA(2589, 15641, F25, 30) (dual of [15641, 15552, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(25107, 15706, F25, 30) (dual of [15706, 15599, 31]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(25108, 15708, F25, 30) (dual of [15708, 15600, 31]-code) | [i] | ||
| 4 | Linear OOA(2588, 10371, F25, 2, 30) (dual of [(10371, 2), 20654, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (58, 88, 10371)-net over F25 | [i] | ||
| 6 | Linear OOA(2588, 7820, F25, 2, 30) (dual of [(7820, 2), 15552, 31]-NRT-code) | [i] | OOA Folding | |