Information on Result #675942
Linear OA(3194, 2205, F3, 41) (dual of [2205, 2011, 42]-code), using construction X applied to Ce(40) ⊂ Ce(37) 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(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(34, 18, F3, 2) (dual of [18, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-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(3194, 1732, F3, 2, 41) (dual of [(1732, 2), 3270, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3194, 1732, F3, 3, 41) (dual of [(1732, 3), 5002, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3194, 1732, F3, 4, 41) (dual of [(1732, 4), 6734, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3194, 1732, F3, 5, 41) (dual of [(1732, 5), 8466, 42]-NRT-code) | [i] | ||
| 5 | Digital (153, 194, 1732)-net over F3 | [i] | ||
| 6 | Linear OOA(3194, 1102, F3, 2, 41) (dual of [(1102, 2), 2010, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3194, 735, F3, 3, 41) (dual of [(735, 3), 2011, 42]-NRT-code) | [i] | ||
| 8 | Linear OOA(3194, 551, F3, 4, 41) (dual of [(551, 4), 2010, 42]-NRT-code) | [i] | ||
| 9 | Linear OOA(3194, 441, F3, 5, 41) (dual of [(441, 5), 2011, 42]-NRT-code) | [i] | ||