Information on Result #991409
Linear OOA(8142, 2189, F81, 3, 21) (dual of [(2189, 3), 6525, 22]-NRT-code), using OOA 3-folding based on linear OA(8142, 6567, F81, 21) (dual of [6567, 6525, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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(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(8143, 2189, F81, 3, 21) (dual of [(2189, 3), 6524, 22]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(8154, 2305, F81, 3, 21) (dual of [(2305, 3), 6861, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 3 | Linear OOA(8142, 2136, F81, 4, 21) (dual of [(2136, 4), 8502, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (21, 42, 2136)-net over F81 | [i] | ||