Information on Result #675953
Linear OA(3159, 2205, F3, 34) (dual of [2205, 2046, 35]-code), using construction X applied to Ce(33) ⊂ Ce(30) based on
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3141, 2187, F3, 31) (dual of [2187, 2046, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(3160, 2206, F3, 34) (dual of [2206, 2046, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3159, 1422, F3, 2, 34) (dual of [(1422, 2), 2685, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3159, 1422, F3, 3, 34) (dual of [(1422, 3), 4107, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(3159, 1422, F3, 4, 34) (dual of [(1422, 4), 5529, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(3159, 1422, F3, 5, 34) (dual of [(1422, 5), 6951, 35]-NRT-code) | [i] | ||
| 6 | Digital (125, 159, 1422)-net over F3 | [i] | ||
| 7 | Linear OOA(3159, 1102, F3, 2, 34) (dual of [(1102, 2), 2045, 35]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3159, 735, F3, 3, 34) (dual of [(735, 3), 2046, 35]-NRT-code) | [i] | ||
| 9 | Linear OOA(3159, 551, F3, 4, 34) (dual of [(551, 4), 2045, 35]-NRT-code) | [i] | ||
| 10 | Linear OOA(3159, 441, F3, 5, 34) (dual of [(441, 5), 2046, 35]-NRT-code) | [i] | ||