Information on Result #2174757
There is no linear OA(2151, 174, F2, 74) (dual of [174, 23, 75]-code), because 4 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(2152, 174, F2, 2, 75) (dual of [(174, 2), 196, 76]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2151, 174, F2, 2, 74) (dual of [(174, 2), 197, 75]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2151, 174, F2, 3, 74) (dual of [(174, 3), 371, 75]-NRT-code) | [i] | ||
| 4 | No linear OOA(2151, 174, F2, 4, 74) (dual of [(174, 4), 545, 75]-NRT-code) | [i] | ||
| 5 | No linear OOA(2151, 174, F2, 5, 74) (dual of [(174, 5), 719, 75]-NRT-code) | [i] | ||
| 6 | No linear OOA(2151, 174, F2, 6, 74) (dual of [(174, 6), 893, 75]-NRT-code) | [i] | ||
| 7 | No linear OOA(2151, 174, F2, 7, 74) (dual of [(174, 7), 1067, 75]-NRT-code) | [i] | ||
| 8 | No linear OOA(2151, 174, F2, 8, 74) (dual of [(174, 8), 1241, 75]-NRT-code) | [i] | ||
| 9 | No digital (77, 151, 174)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |