Information on Result #879968
Linear OOA(25614, 32771, F256, 2, 7) (dual of [(32771, 2), 65528, 8]-NRT-code), using OOA 2-folding based on linear OA(25614, 65542, F256, 7) (dual of [65542, 65528, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2569, 65537, F256, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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, s, F256, 1) (dual of [s, s−1, 2]-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(25618, 65542, F256, 2, 7) (dual of [(65542, 2), 131066, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(25654, 4227072, F256, 2, 14) (dual of [(4227072, 2), 8454090, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(25657, 4227072, F256, 2, 15) (dual of [(4227072, 2), 8454087, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(25614, 32771, F256, 3, 7) (dual of [(32771, 3), 98299, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(25614, 32771, F256, 4, 7) (dual of [(32771, 4), 131070, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(25614, 32771, F256, 5, 7) (dual of [(32771, 5), 163841, 8]-NRT-code) | [i] | ||
| 7 | Linear OOA(25614, 32771, F256, 6, 7) (dual of [(32771, 6), 196612, 8]-NRT-code) | [i] | ||