Information on Result #2174771
There is no linear OA(2164, 193, F2, 78) (dual of [193, 29, 79]-code), because 2 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(2165, 193, F2, 2, 79) (dual of [(193, 2), 221, 80]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2166, 193, F2, 2, 80) (dual of [(193, 2), 220, 81]-NRT-code) | [i] | ||
| 3 | No linear OOA(2167, 193, F2, 2, 81) (dual of [(193, 2), 219, 82]-NRT-code) | [i] | ||
| 4 | No linear OOA(2164, 193, F2, 2, 78) (dual of [(193, 2), 222, 79]-NRT-code) | [i] | Depth Reduction | |
| 5 | No linear OOA(2164, 193, F2, 3, 78) (dual of [(193, 3), 415, 79]-NRT-code) | [i] | ||
| 6 | No linear OOA(2164, 193, F2, 4, 78) (dual of [(193, 4), 608, 79]-NRT-code) | [i] | ||
| 7 | No linear OOA(2164, 193, F2, 5, 78) (dual of [(193, 5), 801, 79]-NRT-code) | [i] | ||
| 8 | No linear OOA(2164, 193, F2, 6, 78) (dual of [(193, 6), 994, 79]-NRT-code) | [i] | ||
| 9 | No linear OOA(2164, 193, F2, 7, 78) (dual of [(193, 7), 1187, 79]-NRT-code) | [i] | ||
| 10 | No linear OOA(2164, 193, F2, 8, 78) (dual of [(193, 8), 1380, 79]-NRT-code) | [i] | ||
| 11 | No digital (86, 164, 193)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |