Information on Result #722930
Linear OA(2577, 322, F25, 41) (dual of [322, 245, 42]-code), using construction XX applied to C1 = C([0,39]), C2 = C([4,40]), C3 = C1 + C2 = C([4,39]), and C∩ = C1 ∩ C2 = C([0,40]) based on
- linear OA(2572, 312, F25, 40) (dual of [312, 240, 41]-code), using the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2569, 312, F25, 37) (dual of [312, 243, 38]-code), using the BCH-code C(I) with length 312 | 252−1, defining interval I = {4,5,…,40}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2574, 312, F25, 41) (dual of [312, 238, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2567, 312, F25, 36) (dual of [312, 245, 37]-code), using the BCH-code C(I) with length 312 | 252−1, defining interval I = {4,5,…,39}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(253, 8, F25, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,25) or 8-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(2577, 161, F25, 2, 41) (dual of [(161, 2), 245, 42]-NRT-code) | [i] | OOA Folding | |