Information on Result #730812
Linear OA(25629, 776, F256, 17) (dual of [776, 747, 18]-code), using construction XX applied to C1 = C([121,136]), C2 = C([120,134]), C3 = C1 + C2 = C([121,134]), and C∩ = C1 ∩ C2 = C([120,136]) based on
- linear OA(25626, 771, F256, 16) (dual of [771, 745, 17]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {121,122,…,136}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(25626, 771, F256, 15) (dual of [771, 745, 16]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {120,121,…,134}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25628, 771, F256, 17) (dual of [771, 743, 18]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {120,121,…,136}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25624, 771, F256, 14) (dual of [771, 747, 15]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {121,122,…,134}, and designed minimum distance d ≥ |I|+1 = 15 [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(25629, 776, F256, 2, 17) (dual of [(776, 2), 1523, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25629, 776, F256, 3, 17) (dual of [(776, 3), 2299, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(25629, 776, F256, 4, 17) (dual of [(776, 4), 3075, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(25629, 776, F256, 5, 17) (dual of [(776, 5), 3851, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(25629, 776, F256, 6, 17) (dual of [(776, 6), 4627, 18]-NRT-code) | [i] | ||
| 6 | Digital (12, 29, 776)-net over F256 | [i] | ||
| 7 | Linear OOA(25629, 388, F256, 2, 17) (dual of [(388, 2), 747, 18]-NRT-code) | [i] | OOA Folding | |