Information on Result #694715
Linear OA(2554, 57, F25, 51) (dual of [57, 3, 52]-code), using construction X applied to C([0,90]) ⊂ C([0,86]) based on
- linear OA(2551, 52, F25, 51) (dual of [52, 1, 52]-code or 52-arc in PG(50,25)), using contraction [i] based on linear OA(25103, 104, F25, 103) (dual of [104, 1, 104]-code or 104-arc in PG(102,25)), using the expurgated narrow-sense BCH-code C(I) with length 104 | 252−1, defining interval I = [0,90], and minimum distance d ≥ |{2,17,32,…,−28}|+1 = 104 (BCH-bound) [i]
- linear OA(2549, 52, F25, 47) (dual of [52, 3, 48]-code), using contraction [i] based on linear OA(25101, 104, F25, 95) (dual of [104, 3, 96]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 252−1, defining interval I = [0,86], and minimum distance d ≥ |{−8,−7,…,86}|+1 = 96 (BCH-bound) [i]
- linear OA(253, 5, F25, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,25) or 5-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 OA(2553, 56, F25, 50) (dual of [56, 3, 51]-code) | [i] | Truncation | |
| 2 | Linear OA(2550, 53, F25, 47) (dual of [53, 3, 48]-code) | [i] | ||
| 3 | Linear OOA(2554, 28, F25, 2, 51) (dual of [(28, 2), 2, 52]-NRT-code) | [i] | OOA Folding | |