Information on Result #676170
Linear OA(3192, 2197, F3, 41) (dual of [2197, 2005, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(39) ⊂ Ce(37) based on
- linear OA(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- 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(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3192, 1635, F3, 2, 41) (dual of [(1635, 2), 3078, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3192, 1635, F3, 3, 41) (dual of [(1635, 3), 4713, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3192, 1635, F3, 4, 41) (dual of [(1635, 4), 6348, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3192, 1635, F3, 5, 41) (dual of [(1635, 5), 7983, 42]-NRT-code) | [i] | ||
| 5 | Digital (151, 192, 1635)-net over F3 | [i] | ||
| 6 | Linear OOA(3192, 732, F3, 3, 41) (dual of [(732, 3), 2004, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3192, 549, F3, 4, 41) (dual of [(549, 4), 2004, 42]-NRT-code) | [i] | ||