Information on Result #693562
Linear OA(2559, 15644, F25, 19) (dual of [15644, 15585, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
- linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(2559, 15644, F25, 2, 19) (dual of [(15644, 2), 31229, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (40, 59, 15644)-net over F25 | [i] | ||
| 3 | Linear OOA(2559, 7822, F25, 2, 19) (dual of [(7822, 2), 15585, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2559, 1738, F25, 19, 19) (dual of [(1738, 19), 32963, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |