Information on Result #694723
Linear OA(2782, 531451, F27, 21) (dual of [531451, 531369, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(2781, 531442, F27, 21) (dual of [531442, 531361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2773, 531442, F27, 19) (dual of [531442, 531369, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 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 | Linear OA(2794, 531499, F27, 21) (dual of [531499, 531405, 22]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2796, 531515, F27, 21) (dual of [531515, 531419, 22]-code) | [i] | ||
| 3 | OA(2798, 531567, S27, 21) | [i] | ||
| 4 | Linear OOA(2782, 385799, F27, 2, 21) (dual of [(385799, 2), 771516, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (61, 82, 385799)-net over F27 | [i] | ||
| 6 | Linear OOA(2782, 265725, F27, 2, 21) (dual of [(265725, 2), 531368, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2782, 53145, F27, 21, 21) (dual of [(53145, 21), 1115963, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |