Information on Result #675818
Linear OA(3205, 2224, F3, 42) (dual of [2224, 2019, 43]-code), using construction X applied to C([0,21]) ⊂ C([0,18]) based on
- linear OA(3197, 2188, F3, 43) (dual of [2188, 1991, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(38, 36, F3, 4) (dual of [36, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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 OA(3209, 2228, F3, 42) (dual of [2228, 2019, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3210, 2229, F3, 42) (dual of [2229, 2019, 43]-code) | [i] | ||
| 3 | Linear OOA(3205, 2101, F3, 2, 42) (dual of [(2101, 2), 3997, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3205, 2101, F3, 3, 42) (dual of [(2101, 3), 6098, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(3205, 2101, F3, 4, 42) (dual of [(2101, 4), 8199, 43]-NRT-code) | [i] | ||
| 6 | Linear OOA(3205, 2101, F3, 5, 42) (dual of [(2101, 5), 10300, 43]-NRT-code) | [i] | ||
| 7 | Digital (163, 205, 2101)-net over F3 | [i] | ||
| 8 | Linear OA(3207, 2227, F3, 42) (dual of [2227, 2020, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(3208, 2229, F3, 42) (dual of [2229, 2021, 43]-code) | [i] | ||
| 10 | Linear OA(3209, 2231, F3, 42) (dual of [2231, 2022, 43]-code) | [i] | ||
| 11 | Linear OOA(3205, 1112, F3, 2, 42) (dual of [(1112, 2), 2019, 43]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3205, 741, F3, 3, 42) (dual of [(741, 3), 2018, 43]-NRT-code) | [i] | ||
| 13 | Linear OOA(3205, 556, F3, 4, 42) (dual of [(556, 4), 2019, 43]-NRT-code) | [i] | ||
| 14 | Linear OOA(3205, 444, F3, 5, 42) (dual of [(444, 5), 2015, 43]-NRT-code) | [i] | ||