Information on Result #2174763
There is no linear OA(2160, 193, F2, 76) (dual of [193, 33, 77]-code), because 3 times code embedding in larger space would yield linear OA(2163, 196, F2, 76) (dual of [196, 33, 77]-code), but
- adding a parity check bit [i] would yield linear OA(2164, 197, F2, 77) (dual of [197, 33, 78]-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, 193, F2, 2, 77) (dual of [(193, 2), 225, 78]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2160, 193, F2, 2, 76) (dual of [(193, 2), 226, 77]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2160, 193, F2, 3, 76) (dual of [(193, 3), 419, 77]-NRT-code) | [i] | ||
| 4 | No linear OOA(2160, 193, F2, 4, 76) (dual of [(193, 4), 612, 77]-NRT-code) | [i] | ||
| 5 | No linear OOA(2160, 193, F2, 5, 76) (dual of [(193, 5), 805, 77]-NRT-code) | [i] | ||
| 6 | No linear OOA(2160, 193, F2, 6, 76) (dual of [(193, 6), 998, 77]-NRT-code) | [i] | ||
| 7 | No linear OOA(2160, 193, F2, 7, 76) (dual of [(193, 7), 1191, 77]-NRT-code) | [i] | ||
| 8 | No linear OOA(2160, 193, F2, 8, 76) (dual of [(193, 8), 1384, 77]-NRT-code) | [i] | ||
| 9 | No digital (84, 160, 193)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |