Information on Result #814579
Linear OOA(3146, 3289, F3, 2, 27) (dual of [(3289, 2), 6432, 28]-NRT-code), using OOA 2-folding based on linear OA(3146, 6578, F3, 27) (dual of [6578, 6432, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3146, 6579, F3, 27) (dual of [6579, 6433, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(3145, 6562, F3, 27) (dual of [6562, 6417, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3129, 6562, F3, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [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(3146, 3289, F3, 3, 27) (dual of [(3289, 3), 9721, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3146, 3289, F3, 4, 27) (dual of [(3289, 4), 13010, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3146, 3289, F3, 5, 27) (dual of [(3289, 5), 16299, 28]-NRT-code) | [i] | ||
| 4 | Digital (119, 146, 3289)-net over F3 | [i] | ||