Information on Result #694963
Linear OA(2780, 19691, F27, 27) (dual of [19691, 19611, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(2779, 19684, F27, 27) (dual of [19684, 19605, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(2773, 19684, F27, 25) (dual of [19684, 19611, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 | OA(27100, 19807, S27, 27) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(2780, 13042, F27, 2, 27) (dual of [(13042, 2), 26004, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (53, 80, 13042)-net over F27 | [i] | ||
| 4 | Linear OOA(2780, 9845, F27, 2, 27) (dual of [(9845, 2), 19610, 28]-NRT-code) | [i] | OOA Folding | |