Information on Result #547937
There is no linear OA(541, 52, F5, 33) (dual of [52, 11, 34]-code), because construction Y1 would yield
- linear OA(540, 44, F5, 33) (dual of [44, 4, 34]-code), but
- OA(511, 52, S5, 8), but
- discarding factors would yield OA(511, 48, S5, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 50 937665 > 511 [i]
- discarding factors would yield OA(511, 48, S5, 8), 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 OOA(542, 52, F5, 2, 34) (dual of [(52, 2), 62, 35]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(541, 52, F5, 2, 33) (dual of [(52, 2), 63, 34]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(541, 52, F5, 3, 33) (dual of [(52, 3), 115, 34]-NRT-code) | [i] | ||
| 4 | No digital (8, 41, 52)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |