Information on Result #694724
Linear OA(2774, 531451, F27, 19) (dual of [531451, 531377, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- 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(2765, 531442, F27, 17) (dual of [531442, 531377, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(2785, 531499, F27, 19) (dual of [531499, 531414, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2787, 531515, F27, 19) (dual of [531515, 531428, 20]-code) | [i] | ||
| 3 | OA(2786, 531533, S27, 19) | [i] | ||
| 4 | Linear OOA(2774, 386729, F27, 2, 19) (dual of [(386729, 2), 773384, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (55, 74, 386729)-net over F27 | [i] | ||
| 6 | Linear OOA(2774, 265725, F27, 2, 19) (dual of [(265725, 2), 531376, 20]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2774, 59050, F27, 19, 19) (dual of [(59050, 19), 1121876, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |