Information on Result #724706
Linear OA(2578, 634, F25, 40) (dual of [634, 556, 41]-code), using construction XX applied to C1 = C([621,35]), C2 = C([0,36]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([621,36]) based on
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,35}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,36}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(25102, 700, F25, 40) (dual of [700, 598, 41]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(25103, 702, F25, 40) (dual of [702, 599, 41]-code) | [i] | ||
| 3 | Linear OA(25104, 704, F25, 40) (dual of [704, 600, 41]-code) | [i] | ||
| 4 | Linear OA(25108, 760, F25, 40) (dual of [760, 652, 41]-code) | [i] | ||
| 5 | Linear OOA(2578, 317, F25, 2, 40) (dual of [(317, 2), 556, 41]-NRT-code) | [i] | OOA Folding | |