Information on Result #693569
Linear OA(2538, 15644, F25, 12) (dual of [15644, 15606, 13]-code), using construction X applied to Ce(11) ⊂ Ce(6) based on
- linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2519, 15625, F25, 7) (dual of [15625, 15606, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(254, 19, F25, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), 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(2538, 15644, F25, 2, 12) (dual of [(15644, 2), 31250, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (26, 38, 15644)-net over F25 | [i] | ||
| 3 | Linear OOA(2538, 7822, F25, 2, 12) (dual of [(7822, 2), 15606, 13]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2538, 2607, F25, 12, 12) (dual of [(2607, 12), 31246, 13]-NRT-code) | [i] | OA Folding and Stacking | |