Information on Result #992020
Linear OOA(8182, 2189, F81, 3, 41) (dual of [(2189, 3), 6485, 42]-NRT-code), using OOA 3-folding based on linear OA(8182, 6567, F81, 41) (dual of [6567, 6485, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,19]) [i] based on
- linear OA(8181, 6562, F81, 41) (dual of [6562, 6481, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(8177, 6562, F81, 39) (dual of [6562, 6485, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (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(8182, 2158, F81, 4, 41) (dual of [(2158, 4), 8550, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (41, 82, 2158)-net over F81 | [i] | ||