Information on Result #694982
Linear OA(2782, 19699, F27, 27) (dual of [19699, 19617, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,11]) 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(2767, 19684, F27, 23) (dual of [19684, 19617, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), 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(2782, 16981, F27, 2, 27) (dual of [(16981, 2), 33880, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (55, 82, 16981)-net over F27 | [i] | ||
| 3 | Linear OOA(2782, 9849, F27, 2, 27) (dual of [(9849, 2), 19616, 28]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2782, 1515, F27, 27, 27) (dual of [(1515, 27), 40823, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |