Information on Result #694735
Linear OA(2718, 531452, F27, 5) (dual of [531452, 531434, 6]-code), using construction X4 applied to C([0,2]) ⊂ C([0,1]) based on
- linear OA(2717, 531442, F27, 5) (dual of [531442, 531425, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(279, 531442, F27, 3) (dual of [531442, 531433, 4]-code or 531442-cap in PG(8,27)), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(279, 10, F27, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,27)), using
- dual of repetition code with length 10 [i]
- linear OA(271, 10, F27, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), 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(2718, 531452, F27, 2, 5) (dual of [(531452, 2), 1062886, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (13, 18, 531452)-net over F27 | [i] | ||
| 3 | Linear OOA(2718, 265726, F27, 2, 5) (dual of [(265726, 2), 531434, 6]-NRT-code) | [i] | OOA Folding | |