Information on Result #676015
Linear OA(3191, 2216, F3, 40) (dual of [2216, 2025, 41]-code), using construction X applied to Ce(39) ⊂ Ce(34) based on
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [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(38, 29, F3, 4) (dual of [29, 21, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3191, 1790, F3, 2, 40) (dual of [(1790, 2), 3389, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3191, 1790, F3, 3, 40) (dual of [(1790, 3), 5179, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(3191, 1790, F3, 4, 40) (dual of [(1790, 4), 6969, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3191, 1790, F3, 5, 40) (dual of [(1790, 5), 8759, 41]-NRT-code) | [i] | ||
| 5 | Digital (151, 191, 1790)-net over F3 | [i] | ||
| 6 | Linear OOA(3191, 1108, F3, 2, 40) (dual of [(1108, 2), 2025, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3191, 554, F3, 4, 40) (dual of [(554, 4), 2025, 41]-NRT-code) | [i] | ||
| 8 | Linear OOA(3191, 443, F3, 5, 40) (dual of [(443, 5), 2024, 41]-NRT-code) | [i] | ||