Information on Result #2234353
Linear OA(3169, 2194, F3, 36) (dual of [2194, 2025, 37]-code), using 1 times truncation based on linear OA(3170, 2195, F3, 37) (dual of [2195, 2025, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- 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(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(31, 8, F3, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3169, 1510, F3, 2, 36) (dual of [(1510, 2), 2851, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3169, 1510, F3, 3, 36) (dual of [(1510, 3), 4361, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3169, 1510, F3, 4, 36) (dual of [(1510, 4), 5871, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3169, 1510, F3, 5, 36) (dual of [(1510, 5), 7381, 37]-NRT-code) | [i] | ||
| 5 | Digital (133, 169, 1510)-net over F3 | [i] | ||
| 6 | Linear OOA(3169, 1097, F3, 2, 36) (dual of [(1097, 2), 2025, 37]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3169, 731, F3, 3, 36) (dual of [(731, 3), 2024, 37]-NRT-code) | [i] | ||
| 8 | Linear OOA(3169, 548, F3, 4, 36) (dual of [(548, 4), 2023, 37]-NRT-code) | [i] | ||
| 9 | Linear OOA(3169, 438, F3, 5, 36) (dual of [(438, 5), 2021, 37]-NRT-code) | [i] | ||