Information on Result #694974
Linear OA(2720, 19692, F27, 7) (dual of [19692, 19672, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(2719, 19684, F27, 7) (dual of [19684, 19665, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2713, 19684, F27, 5) (dual of [19684, 19671, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(277, 8, F27, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,27)), using
- dual of repetition code with length 8 [i]
- linear OA(271, 8, F27, 1) (dual of [8, 7, 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 | OA(930, 19692, S9, 7) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(2720, 19692, F27, 2, 7) (dual of [(19692, 2), 39364, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (13, 20, 19692)-net over F27 | [i] | ||
| 4 | Linear OOA(2720, 9846, F27, 2, 7) (dual of [(9846, 2), 19672, 8]-NRT-code) | [i] | OOA Folding | |