Information on Result #726602
Linear OA(2794, 782, F27, 40) (dual of [782, 688, 41]-code), using construction XX applied to C1 = C([726,28]), C2 = C([9,37]), C3 = C1 + C2 = C([9,28]), and C∩ = C1 ∩ C2 = C([726,37]) based on
- linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2757, 728, F27, 29) (dual of [728, 671, 30]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {9,10,…,37}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2776, 728, F27, 40) (dual of [728, 652, 41]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,37}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {9,10,…,28}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2710, 28, F27, 10) (dual of [28, 18, 11]-code or 28-arc in PG(9,27)), using
- extended Reed–Solomon code RSe(18,27) [i]
- linear OA(278, 26, F27, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,27)), using
- discarding factors / shortening the dual code based on linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)), using
- Reed–Solomon code RS(19,27) [i]
- discarding factors / shortening the dual code based on linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)), 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(2794, 391, F27, 2, 40) (dual of [(391, 2), 688, 41]-NRT-code) | [i] | OOA Folding | |