Information on Result #730855
Linear OA(25644, 776, F256, 26) (dual of [776, 732, 27]-code), using construction XX applied to C1 = C([245,269]), C2 = C([244,267]), C3 = C1 + C2 = C([245,267]), and C∩ = C1 ∩ C2 = C([244,269]) based on
- linear OA(25641, 771, F256, 25) (dual of [771, 730, 26]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {245,246,…,269}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25641, 771, F256, 24) (dual of [771, 730, 25]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,267}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25643, 771, F256, 26) (dual of [771, 728, 27]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,269}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25639, 771, F256, 23) (dual of [771, 732, 24]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {245,246,…,267}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 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 | Linear OOA(25644, 776, F256, 2, 26) (dual of [(776, 2), 1508, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25644, 776, F256, 3, 26) (dual of [(776, 3), 2284, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(25644, 776, F256, 4, 26) (dual of [(776, 4), 3060, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(25644, 776, F256, 5, 26) (dual of [(776, 5), 3836, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(25644, 776, F256, 6, 26) (dual of [(776, 6), 4612, 27]-NRT-code) | [i] | ||
| 6 | Digital (18, 44, 776)-net over F256 | [i] | ||
| 7 | Linear OOA(25644, 388, F256, 2, 26) (dual of [(388, 2), 732, 27]-NRT-code) | [i] | OOA Folding | |