Information on Result #694141
Linear OA(2553, 637, F25, 26) (dual of [637, 584, 27]-code), using construction X applied to Ce(25) ⊂ Ce(20) based on
- linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2541, 625, F25, 21) (dual of [625, 584, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(254, 12, F25, 4) (dual of [12, 8, 5]-code or 12-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(2553, 426, F25, 2, 26) (dual of [(426, 2), 799, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (27, 53, 426)-net over F25 | [i] | ||
| 3 | Linear OOA(2553, 318, F25, 2, 26) (dual of [(318, 2), 583, 27]-NRT-code) | [i] | OOA Folding | |