Information on Result #725306
Linear OA(2788, 189, F27, 51) (dual of [189, 101, 52]-code), using construction XX applied to C1 = C([0,49]), C2 = C([3,50]), C3 = C1 + C2 = C([3,49]), and C∩ = C1 ∩ C2 = C([0,50]) based on
- linear OA(2784, 182, F27, 50) (dual of [182, 98, 51]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2783, 182, F27, 48) (dual of [182, 99, 49]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {3,4,…,50}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(2786, 182, F27, 51) (dual of [182, 96, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2781, 182, F27, 47) (dual of [182, 101, 48]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {3,4,…,49}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(272, 5, F27, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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(2788, 94, F27, 2, 51) (dual of [(94, 2), 100, 52]-NRT-code) | [i] | OOA Folding | |