Information on Result #693543
Linear OA(2531, 15640, F25, 10) (dual of [15640, 15609, 11]-code), using construction X applied to Ce(9) ⊂ Ce(5) based on
- linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(2531, 15640, F25, 2, 10) (dual of [(15640, 2), 31249, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (21, 31, 15640)-net over F25 | [i] | ||
| 3 | Linear OOA(2531, 7820, F25, 2, 10) (dual of [(7820, 2), 15609, 11]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2531, 3128, F25, 10, 10) (dual of [(3128, 10), 31249, 11]-NRT-code) | [i] | OA Folding and Stacking | |