Information on Result #675926
Linear OA(3243, 2205, F3, 52) (dual of [2205, 1962, 53]-code), using construction X applied to Ce(51) ⊂ Ce(48) based on
- linear OA(3239, 2187, F3, 52) (dual of [2187, 1948, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3225, 2187, F3, 49) (dual of [2187, 1962, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [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(3244, 2206, F3, 52) (dual of [2206, 1962, 53]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3243, 1940, F3, 2, 52) (dual of [(1940, 2), 3637, 53]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3243, 1940, F3, 3, 52) (dual of [(1940, 3), 5577, 53]-NRT-code) | [i] | ||
| 4 | Linear OOA(3243, 1940, F3, 4, 52) (dual of [(1940, 4), 7517, 53]-NRT-code) | [i] | ||
| 5 | Linear OOA(3243, 1940, F3, 5, 52) (dual of [(1940, 5), 9457, 53]-NRT-code) | [i] | ||
| 6 | Digital (191, 243, 1940)-net over F3 | [i] | ||
| 7 | Linear OOA(3243, 1102, F3, 2, 52) (dual of [(1102, 2), 1961, 53]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3243, 735, F3, 3, 52) (dual of [(735, 3), 1962, 53]-NRT-code) | [i] | ||
| 9 | Linear OOA(3243, 551, F3, 4, 52) (dual of [(551, 4), 1961, 53]-NRT-code) | [i] | ||
| 10 | Linear OOA(3243, 441, F3, 5, 52) (dual of [(441, 5), 1962, 53]-NRT-code) | [i] | ||