Information on Result #548365
There is no linear OA(2172, 187, F2, 86) (dual of [187, 15, 87]-code), because residual code would yield linear OA(286, 100, F2, 43) (dual of [100, 14, 44]-code), but
- 1 times truncation [i] would yield linear OA(285, 99, F2, 42) (dual of [99, 14, 43]-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 OA(2173, 188, F2, 87) (dual of [188, 15, 88]-code) | [i] | Truncation | |
| 2 | No linear OOA(2173, 187, F2, 2, 87) (dual of [(187, 2), 201, 88]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2172, 187, F2, 2, 86) (dual of [(187, 2), 202, 87]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2172, 187, F2, 3, 86) (dual of [(187, 3), 389, 87]-NRT-code) | [i] | ||
| 5 | No linear OOA(2172, 187, F2, 4, 86) (dual of [(187, 4), 576, 87]-NRT-code) | [i] | ||
| 6 | No linear OOA(2172, 187, F2, 5, 86) (dual of [(187, 5), 763, 87]-NRT-code) | [i] | ||
| 7 | No linear OOA(2172, 187, F2, 6, 86) (dual of [(187, 6), 950, 87]-NRT-code) | [i] | ||
| 8 | No linear OOA(2172, 187, F2, 7, 86) (dual of [(187, 7), 1137, 87]-NRT-code) | [i] | ||
| 9 | No linear OOA(2172, 187, F2, 8, 86) (dual of [(187, 8), 1324, 87]-NRT-code) | [i] | ||
| 10 | No digital (86, 172, 187)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |