Information on Result #991319
Linear OOA(8138, 2189, F81, 3, 19) (dual of [(2189, 3), 6529, 20]-NRT-code), using OOA 3-folding based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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(8139, 2189, F81, 3, 19) (dual of [(2189, 3), 6528, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(8149, 2305, F81, 3, 19) (dual of [(2305, 3), 6866, 20]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 3 | Linear OOA(8138, 2189, F81, 4, 19) (dual of [(2189, 4), 8718, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (19, 38, 2189)-net over F81 | [i] | ||