Information on Result #2266879
Linear OA(3191, 2195, F3, 41) (dual of [2195, 2004, 42]-code), using 1 times code embedding in larger space based on linear OA(3190, 2194, F3, 41) (dual of [2194, 2004, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(39) [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(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-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(3191, 1589, F3, 2, 41) (dual of [(1589, 2), 2987, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3191, 1589, F3, 3, 41) (dual of [(1589, 3), 4576, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3191, 1589, F3, 4, 41) (dual of [(1589, 4), 6165, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3191, 1589, F3, 5, 41) (dual of [(1589, 5), 7754, 42]-NRT-code) | [i] | ||
| 5 | Digital (150, 191, 1589)-net over F3 | [i] | ||
| 6 | Linear OOA(3191, 439, F3, 5, 41) (dual of [(439, 5), 2004, 42]-NRT-code) | [i] | OOA Folding | |