Information on Result #2266749
Linear OA(3249, 19760, F3, 38) (dual of [19760, 19511, 39]-code), using 2 times code embedding in larger space based on linear OA(3247, 19758, F3, 38) (dual of [19758, 19511, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(28) [i] based on
- 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(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(321, 75, F3, 8) (dual of [75, 54, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-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(3249, 13786, F3, 2, 38) (dual of [(13786, 2), 27323, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3249, 13786, F3, 3, 38) (dual of [(13786, 3), 41109, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3249, 13786, F3, 4, 38) (dual of [(13786, 4), 54895, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3249, 13786, F3, 5, 38) (dual of [(13786, 5), 68681, 39]-NRT-code) | [i] | ||
| 5 | Digital (211, 249, 13786)-net over F3 | [i] | ||
| 6 | Linear OOA(3249, 4940, F3, 4, 38) (dual of [(4940, 4), 19511, 39]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3249, 3952, F3, 5, 38) (dual of [(3952, 5), 19511, 39]-NRT-code) | [i] | ||