Information on Result #725056
Linear OA(25106, 881, F25, 38) (dual of [881, 775, 39]-code), using construction XX applied to C1 = C([0,36]), C2 = C([4,37]), C3 = C1 + C2 = C([4,36]), and C∩ = C1 ∩ C2 = C([0,37]) based on
- linear OA(25100, 868, F25, 37) (dual of [868, 768, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 868 | 253−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2596, 868, F25, 34) (dual of [868, 772, 35]-code), using the BCH-code C(I) with length 868 | 253−1, defining interval I = {4,5,…,37}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(25103, 868, F25, 38) (dual of [868, 765, 39]-code), using the expurgated narrow-sense BCH-code C(I) with length 868 | 253−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2593, 868, F25, 33) (dual of [868, 775, 34]-code), using the BCH-code C(I) with length 868 | 253−1, defining interval I = {4,5,…,36}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(253, 10, F25, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,25) or 10-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
- linear OA(250, 3, F25, 0) (dual of [3, 3, 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 OOA(25106, 440, F25, 2, 38) (dual of [(440, 2), 774, 39]-NRT-code) | [i] | OOA Folding | |