Information on Result #2174775
There is no linear OA(2160, 189, F2, 78) (dual of [189, 29, 79]-code), because 6 times code embedding in larger space would yield linear OA(2166, 195, F2, 78) (dual of [195, 29, 79]-code), but
- adding a parity check bit [i] would yield linear OA(2167, 196, F2, 79) (dual of [196, 29, 80]-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(2161, 189, F2, 2, 79) (dual of [(189, 2), 217, 80]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2160, 189, F2, 2, 78) (dual of [(189, 2), 218, 79]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2160, 189, F2, 3, 78) (dual of [(189, 3), 407, 79]-NRT-code) | [i] | ||
| 4 | No linear OOA(2160, 189, F2, 4, 78) (dual of [(189, 4), 596, 79]-NRT-code) | [i] | ||
| 5 | No linear OOA(2160, 189, F2, 5, 78) (dual of [(189, 5), 785, 79]-NRT-code) | [i] | ||
| 6 | No linear OOA(2160, 189, F2, 6, 78) (dual of [(189, 6), 974, 79]-NRT-code) | [i] | ||
| 7 | No linear OOA(2160, 189, F2, 7, 78) (dual of [(189, 7), 1163, 79]-NRT-code) | [i] | ||
| 8 | No linear OOA(2160, 189, F2, 8, 78) (dual of [(189, 8), 1352, 79]-NRT-code) | [i] | ||
| 9 | No digital (82, 160, 189)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |