Information on Result #547833
There is no linear OA(437, 46, F4, 28) (dual of [46, 9, 29]-code), because construction Y1 would yield
- linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- OA(49, 46, S4, 6), but
- discarding factors would yield OA(49, 40, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 273901 > 49 [i]
- discarding factors would yield OA(49, 40, S4, 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(438, 47, F4, 29) (dual of [47, 9, 30]-code) | [i] | Truncation | |
| 2 | No linear OOA(438, 46, F4, 2, 29) (dual of [(46, 2), 54, 30]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(437, 46, F4, 2, 28) (dual of [(46, 2), 55, 29]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(437, 46, F4, 3, 28) (dual of [(46, 3), 101, 29]-NRT-code) | [i] | ||
| 5 | No digital (9, 37, 46)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |