Information on Result #548359
There is no linear OA(2168, 180, F2, 84) (dual of [180, 12, 85]-code), because residual code would yield linear OA(284, 95, F2, 42) (dual of [95, 11, 43]-code), but
- adding a parity check bit [i] would yield linear OA(285, 96, F2, 43) (dual of [96, 11, 44]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
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 OA(2169, 181, F2, 85) (dual of [181, 12, 86]-code) | [i] | Truncation | |
| 2 | No linear OOA(2169, 180, F2, 2, 85) (dual of [(180, 2), 191, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2170, 180, F2, 2, 86) (dual of [(180, 2), 190, 87]-NRT-code) | [i] | ||
| 4 | No linear OOA(2171, 180, F2, 2, 87) (dual of [(180, 2), 189, 88]-NRT-code) | [i] | ||
| 5 | No linear OOA(2168, 180, F2, 2, 84) (dual of [(180, 2), 192, 85]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(2168, 180, F2, 3, 84) (dual of [(180, 3), 372, 85]-NRT-code) | [i] | ||
| 7 | No linear OOA(2168, 180, F2, 4, 84) (dual of [(180, 4), 552, 85]-NRT-code) | [i] | ||
| 8 | No linear OOA(2168, 180, F2, 5, 84) (dual of [(180, 5), 732, 85]-NRT-code) | [i] | ||
| 9 | No linear OOA(2168, 180, F2, 6, 84) (dual of [(180, 6), 912, 85]-NRT-code) | [i] | ||
| 10 | No linear OOA(2168, 180, F2, 7, 84) (dual of [(180, 7), 1092, 85]-NRT-code) | [i] | ||
| 11 | No linear OOA(2168, 180, F2, 8, 84) (dual of [(180, 8), 1272, 85]-NRT-code) | [i] | ||
| 12 | No digital (84, 168, 180)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |