Information on Result #726547
Linear OA(2784, 760, F27, 39) (dual of [760, 676, 40]-code), using construction XX applied to C1 = C([719,27]), C2 = C([1,29]), C3 = C1 + C2 = C([1,27]), and C∩ = C1 ∩ C2 = C([719,29]) based on
- linear OA(2771, 728, F27, 37) (dual of [728, 657, 38]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−9,−8,…,27}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2755, 728, F27, 29) (dual of [728, 673, 30]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−9,−8,…,29}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2752, 728, F27, 27) (dual of [728, 676, 28]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(279, 28, F27, 9) (dual of [28, 19, 10]-code or 28-arc in PG(8,27)), using
- extended Reed–Solomon code RSe(19,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(271, 4, F27, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), 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(2784, 380, F27, 2, 39) (dual of [(380, 2), 676, 40]-NRT-code) | [i] | OOA Folding | |