Information on Result #2705924
Linear OOA(8175, 2189, F81, 3, 37) (dual of [(2189, 3), 6492, 38]-NRT-code), using 811 times duplication based on linear OOA(8174, 2189, F81, 3, 37) (dual of [(2189, 3), 6493, 38]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8174, 6567, F81, 37) (dual of [6567, 6493, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,17]) [i] based on
- linear OA(8173, 6562, F81, 37) (dual of [6562, 6489, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(8169, 6562, F81, 35) (dual of [6562, 6493, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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
- construction X applied to C([0,18]) ⊂ C([0,17]) [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(8175, 2189, F81, 4, 37) (dual of [(2189, 4), 8681, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (38, 75, 2189)-net over F81 | [i] | ||