Information on Result #547659
There is no linear OA(45, 12, F4, 4) (dual of [12, 7, 5]-code), because dual of a near-MDS code is again a near-MDS code would yield linear OA(47, 12, F4, 6) (dual of [12, 5, 7]-code), but
- discarding factors / shortening the dual code would yield linear OA(47, 10, F4, 6) (dual of [10, 3, 7]-code), but
Mode: Bound (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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(46, 13, F4, 5) (dual of [13, 7, 6]-code) | [i] | Truncation | |
| 2 | No linear OOA(46, 12, F4, 2, 5) (dual of [(12, 2), 18, 6]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(45, 12, F4, 2, 4) (dual of [(12, 2), 19, 5]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(45, 12, F4, 3, 4) (dual of [(12, 3), 31, 5]-NRT-code) | [i] | ||
| 5 | No digital (1, 5, 12)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |