Information on Result #693500
Linear OA(2584, 15636, F25, 29) (dual of [15636, 15552, 30]-code), using construction X applied to Ce(28) ⊂ Ce(25) based on
- linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-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(2585, 15637, F25, 29) (dual of [15637, 15552, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(25102, 15702, F25, 29) (dual of [15702, 15600, 30]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(25103, 15704, F25, 29) (dual of [15704, 15601, 30]-code) | [i] | ||
| 4 | Linear OA(25104, 15706, F25, 29) (dual of [15706, 15602, 30]-code) | [i] | ||
| 5 | Linear OOA(2584, 9014, F25, 2, 29) (dual of [(9014, 2), 17944, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (55, 84, 9014)-net over F25 | [i] | ||
| 7 | Linear OOA(2584, 7818, F25, 2, 29) (dual of [(7818, 2), 15552, 30]-NRT-code) | [i] | OOA Folding | |