Information on Result #694972
Linear OA(2726, 19691, F27, 9) (dual of [19691, 19665, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,3]) based on
- 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(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(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(939, 19691, S9, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(2726, 16822, F27, 2, 9) (dual of [(16822, 2), 33618, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (17, 26, 16822)-net over F27 | [i] | ||
| 4 | Linear OOA(2726, 9845, F27, 2, 9) (dual of [(9845, 2), 19664, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2726, 4922, F27, 9, 9) (dual of [(4922, 9), 44272, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |