Information on Result #2266880
Linear OA(3197, 2215, F3, 41) (dual of [2215, 2018, 42]-code), using 1 times code embedding in larger space based on linear OA(3196, 2214, F3, 41) (dual of [2214, 2018, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- linear OA(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(36, 27, F3, 3) (dual of [27, 21, 4]-code or 27-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3197, 1888, F3, 2, 41) (dual of [(1888, 2), 3579, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3197, 1888, F3, 3, 41) (dual of [(1888, 3), 5467, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3197, 1888, F3, 4, 41) (dual of [(1888, 4), 7355, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3197, 1888, F3, 5, 41) (dual of [(1888, 5), 9243, 42]-NRT-code) | [i] | ||
| 5 | Digital (156, 197, 1888)-net over F3 | [i] | ||
| 6 | Linear OOA(3197, 443, F3, 5, 41) (dual of [(443, 5), 2018, 42]-NRT-code) | [i] | OOA Folding | |