Information on Result #2174791
There is no linear OA(2168, 192, F2, 82) (dual of [192, 24, 83]-code), because 4 times code embedding in larger space would yield linear OA(2172, 196, F2, 82) (dual of [196, 24, 83]-code), but
- adding a parity check bit [i] would yield linear OA(2173, 197, F2, 83) (dual of [197, 24, 84]-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 OOA(2169, 192, F2, 2, 83) (dual of [(192, 2), 215, 84]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2168, 192, F2, 2, 82) (dual of [(192, 2), 216, 83]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2168, 192, F2, 3, 82) (dual of [(192, 3), 408, 83]-NRT-code) | [i] | ||
| 4 | No linear OOA(2168, 192, F2, 4, 82) (dual of [(192, 4), 600, 83]-NRT-code) | [i] | ||
| 5 | No linear OOA(2168, 192, F2, 5, 82) (dual of [(192, 5), 792, 83]-NRT-code) | [i] | ||
| 6 | No linear OOA(2168, 192, F2, 6, 82) (dual of [(192, 6), 984, 83]-NRT-code) | [i] | ||
| 7 | No linear OOA(2168, 192, F2, 7, 82) (dual of [(192, 7), 1176, 83]-NRT-code) | [i] | ||
| 8 | No linear OOA(2168, 192, F2, 8, 82) (dual of [(192, 8), 1368, 83]-NRT-code) | [i] | ||
| 9 | No digital (86, 168, 192)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |