Information on Result #2174817
There is no linear OA(2189, 215, F2, 92) (dual of [215, 26, 93]-code), because 5 times code embedding in larger space would yield linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- adding a parity check bit [i] would yield linear OA(2195, 221, F2, 93) (dual of [221, 26, 94]-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(2190, 215, F2, 2, 93) (dual of [(215, 2), 240, 94]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2189, 215, F2, 2, 92) (dual of [(215, 2), 241, 93]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2189, 215, F2, 3, 92) (dual of [(215, 3), 456, 93]-NRT-code) | [i] | ||
| 4 | No linear OOA(2189, 215, F2, 4, 92) (dual of [(215, 4), 671, 93]-NRT-code) | [i] | ||
| 5 | No linear OOA(2189, 215, F2, 5, 92) (dual of [(215, 5), 886, 93]-NRT-code) | [i] | ||
| 6 | No linear OOA(2189, 215, F2, 6, 92) (dual of [(215, 6), 1101, 93]-NRT-code) | [i] | ||
| 7 | No linear OOA(2189, 215, F2, 7, 92) (dual of [(215, 7), 1316, 93]-NRT-code) | [i] | ||
| 8 | No linear OOA(2189, 215, F2, 8, 92) (dual of [(215, 8), 1531, 93]-NRT-code) | [i] | ||
| 9 | No digital (97, 189, 215)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |