Information on Result #730922
Linear OA(25668, 778, F256, 40) (dual of [778, 710, 41]-code), using construction XX applied to C1 = C([239,277]), C2 = C([238,275]), C3 = C1 + C2 = C([239,275]), and C∩ = C1 ∩ C2 = C([238,277]) based on
- linear OA(25665, 771, F256, 39) (dual of [771, 706, 40]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {239,240,…,277}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(25663, 771, F256, 38) (dual of [771, 708, 39]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {238,239,…,275}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(25667, 771, F256, 40) (dual of [771, 704, 41]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {238,239,…,277}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(25661, 771, F256, 37) (dual of [771, 710, 38]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {239,240,…,275}, and designed minimum distance d ≥ |I|+1 = 38 [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(12878, 778, S128, 40) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25668, 389, F256, 2, 40) (dual of [(389, 2), 710, 41]-NRT-code) | [i] | OOA Folding | |