Information on Result #695002
Linear OA(2748, 19707, F27, 15) (dual of [19707, 19659, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,4]) based on
- linear OA(2743, 19684, F27, 15) (dual of [19684, 19641, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(2725, 19684, F27, 9) (dual of [19684, 19659, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(275, 23, F27, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,27)), using
- discarding factors / shortening the dual code based on linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), using
- Reed–Solomon code RS(22,27) [i]
- discarding factors / shortening the dual code based on linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), 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(2748, 19707, F27, 2, 15) (dual of [(19707, 2), 39366, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (33, 48, 19707)-net over F27 | [i] | ||
| 3 | Linear OOA(2748, 9853, F27, 2, 15) (dual of [(9853, 2), 19658, 16]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2748, 2815, F27, 15, 15) (dual of [(2815, 15), 42177, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |