Information on Result #2174799
There is no linear OA(2176, 206, F2, 84) (dual of [206, 30, 85]-code), because 3 times code embedding in larger space would yield linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-code), but
- adding a parity check bit [i] would yield linear OA(2180, 210, F2, 85) (dual of [210, 30, 86]-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(2177, 206, F2, 2, 85) (dual of [(206, 2), 235, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2178, 206, F2, 2, 86) (dual of [(206, 2), 234, 87]-NRT-code) | [i] | ||
| 3 | No linear OOA(2179, 206, F2, 2, 87) (dual of [(206, 2), 233, 88]-NRT-code) | [i] | ||
| 4 | No linear OOA(2176, 206, F2, 2, 84) (dual of [(206, 2), 236, 85]-NRT-code) | [i] | Depth Reduction | |
| 5 | No linear OOA(2176, 206, F2, 3, 84) (dual of [(206, 3), 442, 85]-NRT-code) | [i] | ||
| 6 | No linear OOA(2176, 206, F2, 4, 84) (dual of [(206, 4), 648, 85]-NRT-code) | [i] | ||
| 7 | No linear OOA(2176, 206, F2, 5, 84) (dual of [(206, 5), 854, 85]-NRT-code) | [i] | ||
| 8 | No linear OOA(2176, 206, F2, 6, 84) (dual of [(206, 6), 1060, 85]-NRT-code) | [i] | ||
| 9 | No linear OOA(2176, 206, F2, 7, 84) (dual of [(206, 7), 1266, 85]-NRT-code) | [i] | ||
| 10 | No linear OOA(2176, 206, F2, 8, 84) (dual of [(206, 8), 1472, 85]-NRT-code) | [i] | ||
| 11 | No digital (92, 176, 206)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |