Information on Result #675944
Linear OA(3187, 2205, F3, 40) (dual of [2205, 2018, 41]-code), using construction X applied to Ce(39) ⊂ Ce(36) based on
- 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(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(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 OA(3188, 2206, F3, 40) (dual of [2206, 2018, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3187, 1591, F3, 2, 40) (dual of [(1591, 2), 2995, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3187, 1591, F3, 3, 40) (dual of [(1591, 3), 4586, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3187, 1591, F3, 4, 40) (dual of [(1591, 4), 6177, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(3187, 1591, F3, 5, 40) (dual of [(1591, 5), 7768, 41]-NRT-code) | [i] | ||
| 6 | Digital (147, 187, 1591)-net over F3 | [i] | ||
| 7 | Linear OOA(3187, 1102, F3, 2, 40) (dual of [(1102, 2), 2017, 41]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3187, 735, F3, 3, 40) (dual of [(735, 3), 2018, 41]-NRT-code) | [i] | ||
| 9 | Linear OOA(3187, 551, F3, 4, 40) (dual of [(551, 4), 2017, 41]-NRT-code) | [i] | ||
| 10 | Linear OOA(3187, 441, F3, 5, 40) (dual of [(441, 5), 2018, 41]-NRT-code) | [i] | ||