Information on Result #993618
Linear OOA(25626, 21847, F256, 3, 13) (dual of [(21847, 3), 65515, 14]-NRT-code), using OOA 3-folding based on linear OA(25626, 65541, F256, 13) (dual of [65541, 65515, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
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(25661, 5592832, F256, 3, 13) (dual of [(5592832, 3), 16778435, 14]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(25626, 21847, F256, 4, 13) (dual of [(21847, 4), 87362, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25626, 21847, F256, 5, 13) (dual of [(21847, 5), 109209, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(25626, 21847, F256, 6, 13) (dual of [(21847, 6), 131056, 14]-NRT-code) | [i] | ||
| 5 | Digital (13, 26, 21847)-net over F256 | [i] | ||