Information on Result #694953
Linear OA(27110, 19691, F27, 37) (dual of [19691, 19581, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,17]) based on
- linear OA(27109, 19684, F27, 37) (dual of [19684, 19575, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(27103, 19684, F27, 35) (dual of [19684, 19581, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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 | Linear OOA(27110, 15327, F27, 2, 37) (dual of [(15327, 2), 30544, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (73, 110, 15327)-net over F27 | [i] | ||