Information on Result #547668
There is no linear OA(28, 18, F2, 4) (dual of [18, 10, 5]-code), because construction Y1 would yield
- linear OA(27, 12, F2, 4) (dual of [12, 5, 5]-code), but
- OA(210, 18, S2, 6), but
- discarding factors would yield OA(210, 16, S2, 6), but
- the linear programming bound shows that M ≥ 27136 / 21 > 210 [i]
- discarding factors would yield OA(210, 16, S2, 6), 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(29, 19, F2, 5) (dual of [19, 10, 6]-code) | [i] | Truncation | |
| 2 | No linear OOA(28, 18, F2, 2, 4) (dual of [(18, 2), 28, 5]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(28, 18, F2, 3, 4) (dual of [(18, 3), 46, 5]-NRT-code) | [i] | ||
| 4 | No linear OOA(28, 18, F2, 4, 4) (dual of [(18, 4), 64, 5]-NRT-code) | [i] | ||
| 5 | No linear OOA(28, 18, F2, 5, 4) (dual of [(18, 5), 82, 5]-NRT-code) | [i] | ||
| 6 | No linear OOA(28, 18, F2, 6, 4) (dual of [(18, 6), 100, 5]-NRT-code) | [i] | ||
| 7 | No linear OOA(28, 18, F2, 7, 4) (dual of [(18, 7), 118, 5]-NRT-code) | [i] | ||
| 8 | No linear OOA(28, 18, F2, 8, 4) (dual of [(18, 8), 136, 5]-NRT-code) | [i] | ||
| 9 | No digital (4, 8, 18)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |