Information on Result #2266971
Linear OA(3239, 6608, F3, 43) (dual of [6608, 6369, 44]-code), using 3 times code embedding in larger space based on linear OA(3236, 6605, F3, 43) (dual of [6605, 6369, 44]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), 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(3239, 4709, F3, 2, 43) (dual of [(4709, 2), 9179, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3239, 4709, F3, 3, 43) (dual of [(4709, 3), 13888, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(3239, 4709, F3, 4, 43) (dual of [(4709, 4), 18597, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3239, 4709, F3, 5, 43) (dual of [(4709, 5), 23306, 44]-NRT-code) | [i] | ||
| 5 | Digital (196, 239, 4709)-net over F3 | [i] | ||
| 6 | Linear OOA(3239, 1652, F3, 4, 43) (dual of [(1652, 4), 6369, 44]-NRT-code) | [i] | OOA Folding | |