Information on Result #816404
Linear OOA(3249, 9853, F3, 2, 41) (dual of [(9853, 2), 19457, 42]-NRT-code), using OOA 2-folding based on linear OA(3249, 19706, F3, 41) (dual of [19706, 19457, 42]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3248, 19705, F3, 41) (dual of [19705, 19457, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(37) [i] based on
- linear OA(3244, 19683, F3, 41) (dual of [19683, 19439, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3226, 19683, F3, 38) (dual of [19683, 19457, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(34, 22, F3, 2) (dual of [22, 18, 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
- construction X applied to Ce(40) ⊂ Ce(37) [i] based on
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(3249, 9449, F3, 3, 41) (dual of [(9449, 3), 28098, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3249, 9449, F3, 4, 41) (dual of [(9449, 4), 37547, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3249, 9449, F3, 5, 41) (dual of [(9449, 5), 46996, 42]-NRT-code) | [i] | ||
| 4 | Digital (208, 249, 9449)-net over F3 | [i] | ||