Information on Result #725380
Linear OA(27103, 192, F27, 61) (dual of [192, 89, 62]-code), using construction XX applied to C1 = C([179,56]), C2 = C([0,57]), C3 = C1 + C2 = C([0,56]), and C∩ = C1 ∩ C2 = C([179,57]) based on
- linear OA(2799, 182, F27, 60) (dual of [182, 83, 61]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−3,−2,…,56}, and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(2795, 182, F27, 58) (dual of [182, 87, 59]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,57], and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(27101, 182, F27, 61) (dual of [182, 81, 62]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−3,−2,…,57}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(2793, 182, F27, 57) (dual of [182, 89, 58]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,56], and designed minimum distance d ≥ |I|+1 = 58 [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(27103, 96, F27, 2, 61) (dual of [(96, 2), 89, 62]-NRT-code) | [i] | OOA Folding | |