Information on Result #730904
Linear OA(25663, 778, F256, 37) (dual of [778, 715, 38]-code), using construction XX applied to C1 = C([112,147]), C2 = C([111,145]), C3 = C1 + C2 = C([112,145]), and C∩ = C1 ∩ C2 = C([111,147]) based on
- linear OA(25660, 771, F256, 36) (dual of [771, 711, 37]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {112,113,…,147}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(25658, 771, F256, 35) (dual of [771, 713, 36]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {111,112,…,145}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(25662, 771, F256, 37) (dual of [771, 709, 38]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {111,112,…,147}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(25656, 771, F256, 34) (dual of [771, 715, 35]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {112,113,…,145}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, 256, F256, 1) (dual of [256, 255, 2]-code), using
- Reed–Solomon code RS(255,256) [i]
- discarding factors / shortening the dual code based on linear OA(2561, 256, F256, 1) (dual of [256, 255, 2]-code), using
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 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 | OA(12872, 778, S128, 37) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25663, 389, F256, 2, 37) (dual of [(389, 2), 715, 38]-NRT-code) | [i] | OOA Folding | |