Information on Result #952870
Linear OOA(3180, 1594345, F3, 3, 19) (dual of [(1594345, 3), 4782855, 20]-NRT-code), using OOA 3-folding based on linear OA(3180, 4783035, F3, 19) (dual of [4783035, 4782855, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 4783037, F3, 19) (dual of [4783037, 4782857, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(3113, 4782970, F3, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 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(3180, 1370134, F3, 4, 19) (dual of [(1370134, 4), 5480356, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3180, 1370134, F3, 5, 19) (dual of [(1370134, 5), 6850490, 20]-NRT-code) | [i] | ||
| 3 | Digital (161, 180, 1370134)-net over F3 | [i] | ||