Information on Result #695405
Linear OA(2724, 741, F27, 11) (dual of [741, 717, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- linear OA(2721, 730, F27, 11) (dual of [730, 709, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2713, 730, F27, 7) (dual of [730, 717, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(273, 11, F27, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,27) or 11-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(2724, 722, F27, 2, 11) (dual of [(722, 2), 1420, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (13, 24, 722)-net over F27 | [i] | ||
| 3 | Linear OOA(2724, 370, F27, 2, 11) (dual of [(370, 2), 716, 12]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2724, 148, F27, 11, 11) (dual of [(148, 11), 1604, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |