Information on Result #725226
Linear OA(2774, 192, F27, 41) (dual of [192, 118, 42]-code), using construction XX applied to C1 = C([179,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([179,37]) based on
- linear OA(2770, 182, F27, 40) (dual of [182, 112, 41]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−3,−2,…,36}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2766, 182, F27, 38) (dual of [182, 116, 39]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2772, 182, F27, 41) (dual of [182, 110, 42]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−3,−2,…,37}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2764, 182, F27, 37) (dual of [182, 118, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-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(2774, 96, F27, 2, 41) (dual of [(96, 2), 118, 42]-NRT-code) | [i] | OOA Folding | |