Information on Result #730837
Linear OA(25642, 779, F256, 24) (dual of [779, 737, 25]-code), using construction XX applied to C1 = C([117,139]), C2 = C([116,136]), C3 = C1 + C2 = C([117,136]), and C∩ = C1 ∩ C2 = C([116,139]) based on
- linear OA(25638, 771, F256, 23) (dual of [771, 733, 24]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {117,118,…,139}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25636, 771, F256, 21) (dual of [771, 735, 22]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {116,117,…,136}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25640, 771, F256, 24) (dual of [771, 731, 25]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {116,117,…,139}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25634, 771, F256, 20) (dual of [771, 737, 21]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {117,118,…,136}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2562, 6, F256, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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 | Linear OOA(25642, 389, F256, 2, 24) (dual of [(389, 2), 736, 25]-NRT-code) | [i] | OOA Folding | |