Information on Result #813571
Linear OOA(3120, 9865, F3, 2, 19) (dual of [(9865, 2), 19610, 20]-NRT-code), using OOA 2-folding based on linear OA(3120, 19730, F3, 19) (dual of [19730, 19610, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, 19731, F3, 19) (dual of [19731, 19611, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,9]) ⊂ C([0,6]) [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(3120, 9865, F3, 3, 19) (dual of [(9865, 3), 29475, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3120, 9865, F3, 4, 19) (dual of [(9865, 4), 39340, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(3120, 9865, F3, 5, 19) (dual of [(9865, 5), 49205, 20]-NRT-code) | [i] | ||
| 4 | Digital (101, 120, 9865)-net over F3 | [i] | ||