Information on Result #2174754
There is no linear OA(2154, 177, F2, 74) (dual of [177, 23, 75]-code), because 1 times code embedding in larger space would yield linear OA(2155, 178, F2, 74) (dual of [178, 23, 75]-code), but
- adding a parity check bit [i] would yield linear OA(2156, 179, F2, 75) (dual of [179, 23, 76]-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(2155, 177, F2, 2, 75) (dual of [(177, 2), 199, 76]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2156, 177, F2, 2, 76) (dual of [(177, 2), 198, 77]-NRT-code) | [i] | ||
| 3 | No linear OOA(2157, 177, F2, 2, 77) (dual of [(177, 2), 197, 78]-NRT-code) | [i] | ||
| 4 | No linear OOA(2158, 177, F2, 2, 78) (dual of [(177, 2), 196, 79]-NRT-code) | [i] | ||
| 5 | No linear OOA(2159, 177, F2, 2, 79) (dual of [(177, 2), 195, 80]-NRT-code) | [i] | ||
| 6 | No linear OOA(2154, 177, F2, 2, 74) (dual of [(177, 2), 200, 75]-NRT-code) | [i] | Depth Reduction | |
| 7 | No linear OOA(2154, 177, F2, 3, 74) (dual of [(177, 3), 377, 75]-NRT-code) | [i] | ||
| 8 | No linear OOA(2154, 177, F2, 4, 74) (dual of [(177, 4), 554, 75]-NRT-code) | [i] | ||
| 9 | No linear OOA(2154, 177, F2, 5, 74) (dual of [(177, 5), 731, 75]-NRT-code) | [i] | ||
| 10 | No linear OOA(2154, 177, F2, 6, 74) (dual of [(177, 6), 908, 75]-NRT-code) | [i] | ||
| 11 | No linear OOA(2154, 177, F2, 7, 74) (dual of [(177, 7), 1085, 75]-NRT-code) | [i] | ||
| 12 | No linear OOA(2154, 177, F2, 8, 74) (dual of [(177, 8), 1262, 75]-NRT-code) | [i] | ||
| 13 | No digital (80, 154, 177)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |