Information on Result #670090
Linear OA(8112, 25924, F81, 5) (dual of [25924, 25912, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(811, 6481, F81, 1) (dual of [6481, 6480, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(811, 6481, F81, 1) (dual of [6481, 6480, 2]-code) (see above)
- linear OA(813, 6481, F81, 2) (dual of [6481, 6478, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(813, 6643, F81, 2) (dual of [6643, 6640, 3]-code), using
- Hamming code H(3,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 6643, F81, 2) (dual of [6643, 6640, 3]-code), using
- linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-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(2716, 25924, S27, 5) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(8112, 25924, F81, 2, 5) (dual of [(25924, 2), 51836, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8112, 25924, F81, 3, 5) (dual of [(25924, 3), 77760, 6]-NRT-code) | [i] | ||
| 4 | Linear OOA(8112, 25924, F81, 4, 5) (dual of [(25924, 4), 103684, 6]-NRT-code) | [i] | ||
| 5 | Linear OOA(8112, 12962, F81, 2, 5) (dual of [(12962, 2), 25912, 6]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8112, 12961, F81, 3, 5) (dual of [(12961, 3), 38871, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 7 | Linear OOA(8112, 12961, F81, 4, 5) (dual of [(12961, 4), 51832, 6]-NRT-code) | [i] | ||