Information on Result #675935
Linear OA(3215, 2205, F3, 46) (dual of [2205, 1990, 47]-code), using construction X applied to Ce(45) ⊂ Ce(42) based on
- linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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(3216, 2206, F3, 46) (dual of [2206, 1990, 47]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3215, 1764, F3, 2, 46) (dual of [(1764, 2), 3313, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3215, 1764, F3, 3, 46) (dual of [(1764, 3), 5077, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(3215, 1764, F3, 4, 46) (dual of [(1764, 4), 6841, 47]-NRT-code) | [i] | ||
| 5 | Linear OOA(3215, 1764, F3, 5, 46) (dual of [(1764, 5), 8605, 47]-NRT-code) | [i] | ||
| 6 | Digital (169, 215, 1764)-net over F3 | [i] | ||
| 7 | Linear OOA(3215, 1102, F3, 2, 46) (dual of [(1102, 2), 1989, 47]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3215, 735, F3, 3, 46) (dual of [(735, 3), 1990, 47]-NRT-code) | [i] | ||
| 9 | Linear OOA(3215, 551, F3, 4, 46) (dual of [(551, 4), 1989, 47]-NRT-code) | [i] | ||
| 10 | Linear OOA(3215, 441, F3, 5, 46) (dual of [(441, 5), 1990, 47]-NRT-code) | [i] | ||