Information on Result #694970
Linear OA(2738, 19691, F27, 13) (dual of [19691, 19653, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(2737, 19684, F27, 13) (dual of [19684, 19647, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2731, 19684, F27, 11) (dual of [19684, 19653, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(2746, 19773, S27, 13) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(2738, 12316, F27, 2, 13) (dual of [(12316, 2), 24594, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (25, 38, 12316)-net over F27 | [i] | ||
| 4 | Linear OOA(2738, 9845, F27, 2, 13) (dual of [(9845, 2), 19652, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2738, 3281, F27, 13, 13) (dual of [(3281, 13), 42615, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |