Information on Result #546164
There is no linear OA(238, 45, F2, 20) (dual of [45, 7, 21]-code), because residual code would yield linear OA(218, 24, F2, 10) (dual of [24, 6, 11]-code), but
- residual code [i] would yield linear OA(28, 13, F2, 5) (dual of [13, 5, 6]-code), but
- 1 times truncation [i] would yield linear OA(27, 12, F2, 4) (dual of [12, 5, 5]-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(239, 46, F2, 21) (dual of [46, 7, 22]-code) | [i] | Truncation | |
| 2 | No linear OOA(239, 45, F2, 2, 21) (dual of [(45, 2), 51, 22]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(238, 45, F2, 2, 20) (dual of [(45, 2), 52, 21]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(238, 45, F2, 3, 20) (dual of [(45, 3), 97, 21]-NRT-code) | [i] | ||
| 5 | No linear OOA(238, 45, F2, 4, 20) (dual of [(45, 4), 142, 21]-NRT-code) | [i] | ||
| 6 | No linear OOA(238, 45, F2, 5, 20) (dual of [(45, 5), 187, 21]-NRT-code) | [i] | ||
| 7 | No linear OOA(238, 45, F2, 6, 20) (dual of [(45, 6), 232, 21]-NRT-code) | [i] | ||
| 8 | No linear OOA(238, 45, F2, 7, 20) (dual of [(45, 7), 277, 21]-NRT-code) | [i] | ||
| 9 | No linear OOA(238, 45, F2, 8, 20) (dual of [(45, 8), 322, 21]-NRT-code) | [i] | ||
| 10 | No digital (18, 38, 45)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(278, 86, F2, 40) (dual of [86, 8, 41]-code) | [i] | Residual Code | |
| 12 | No linear OA(239, 49, F2, 20) (dual of [49, 10, 21]-code) | [i] | Construction Y1 (Bound) | |