Information on Result #879987
Linear OOA(25618, 32771, F256, 2, 9) (dual of [(32771, 2), 65524, 10]-NRT-code), using OOA 2-folding based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 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(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(25622, 33028, F256, 2, 9) (dual of [(33028, 2), 66034, 10]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(25618, 31019, F256, 3, 9) (dual of [(31019, 3), 93039, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25618, 31019, F256, 4, 9) (dual of [(31019, 4), 124058, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(25618, 31019, F256, 5, 9) (dual of [(31019, 5), 155077, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(25618, 31019, F256, 6, 9) (dual of [(31019, 6), 186096, 10]-NRT-code) | [i] | ||
| 6 | Digital (9, 18, 31019)-net over F256 | [i] | ||