Information on Result #723005
Linear OA(2598, 320, F25, 54) (dual of [320, 222, 55]-code), using construction XX applied to C1 = C([0,52]), C2 = C([4,53]), C3 = C1 + C2 = C([4,52]), and C∩ = C1 ∩ C2 = C([0,53]) based on
- linear OA(2593, 312, F25, 53) (dual of [312, 219, 54]-code), using the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2592, 312, F25, 50) (dual of [312, 220, 51]-code), using the BCH-code C(I) with length 312 | 252−1, defining interval I = {4,5,…,53}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2595, 312, F25, 54) (dual of [312, 217, 55]-code), using the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,53], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2590, 312, F25, 49) (dual of [312, 222, 50]-code), using the BCH-code C(I) with length 312 | 252−1, defining interval I = {4,5,…,52}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(253, 6, F25, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,25) or 6-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, 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 OOA(2598, 160, F25, 2, 54) (dual of [(160, 2), 222, 55]-NRT-code) | [i] | OOA Folding | |