Information on Result #675951
Linear OA(3166, 2205, F3, 35) (dual of [2205, 2039, 36]-code), using construction X applied to Ce(34) ⊂ Ce(31) based on
- linear OA(3162, 2187, F3, 35) (dual of [2187, 2025, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(3166, 1569, F3, 2, 35) (dual of [(1569, 2), 2972, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3166, 1569, F3, 3, 35) (dual of [(1569, 3), 4541, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(3166, 1569, F3, 4, 35) (dual of [(1569, 4), 6110, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3166, 1569, F3, 5, 35) (dual of [(1569, 5), 7679, 36]-NRT-code) | [i] | ||
| 5 | Digital (131, 166, 1569)-net over F3 | [i] | ||
| 6 | Linear OOA(3166, 1102, F3, 2, 35) (dual of [(1102, 2), 2038, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3166, 735, F3, 3, 35) (dual of [(735, 3), 2039, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(3166, 551, F3, 4, 35) (dual of [(551, 4), 2038, 36]-NRT-code) | [i] | ||
| 9 | Linear OOA(3166, 441, F3, 5, 35) (dual of [(441, 5), 2039, 36]-NRT-code) | [i] | ||