Information on Result #726345
Linear OA(2789, 782, F27, 37) (dual of [782, 693, 38]-code), using construction XX applied to C1 = C([10,36]), C2 = C([0,25]), C3 = C1 + C2 = C([10,25]), and C∩ = C1 ∩ C2 = C([0,36]) based on
- linear OA(2753, 728, F27, 27) (dual of [728, 675, 28]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,36}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2751, 728, F27, 26) (dual of [728, 677, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2770, 728, F27, 37) (dual of [728, 658, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2732, 728, F27, 16) (dual of [728, 696, 17]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {10,11,…,25}, and designed minimum distance d ≥ |I|+1 = 17 [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(279, 26, F27, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,27)), using
- discarding factors / shortening the dual code based on linear OA(279, 27, F27, 9) (dual of [27, 18, 10]-code or 27-arc in PG(8,27)), using
- Reed–Solomon code RS(18,27) [i]
- discarding factors / shortening the dual code based on linear OA(279, 27, F27, 9) (dual of [27, 18, 10]-code or 27-arc in PG(8,27)), 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(2789, 391, F27, 2, 37) (dual of [(391, 2), 693, 38]-NRT-code) | [i] | OOA Folding | |