Information on Result #2487768
Linear OOA(3214, 9867, F3, 2, 34) (dual of [(9867, 2), 19520, 35]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(3210, 9865, F3, 2, 34) (dual of [(9865, 2), 19520, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 19730, F3, 34) (dual of [19730, 19520, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(311, 47, F3, 5) (dual of [47, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [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(3214, 9867, F3, 3, 34) (dual of [(9867, 3), 29387, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3214, 9867, F3, 4, 34) (dual of [(9867, 4), 39254, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3214, 9867, F3, 5, 34) (dual of [(9867, 5), 49121, 35]-NRT-code) | [i] | ||
| 4 | Digital (180, 214, 9867)-net over F3 | [i] | ||