Information on Result #547832
There is no linear OA(432, 41, F4, 24) (dual of [41, 9, 25]-code), because construction Y1 would yield
- linear OA(431, 35, F4, 24) (dual of [35, 4, 25]-code), but
- residual code [i] would yield linear OA(47, 10, F4, 6) (dual of [10, 3, 7]-code), but
- OA(49, 41, 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(433, 42, F4, 25) (dual of [42, 9, 26]-code) | [i] | Truncation | |
| 2 | No linear OA(434, 43, F4, 26) (dual of [43, 9, 27]-code) | [i] | ||
| 3 | No linear OOA(433, 41, F4, 2, 25) (dual of [(41, 2), 49, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(434, 41, F4, 2, 26) (dual of [(41, 2), 48, 27]-NRT-code) | [i] | ||
| 5 | No linear OOA(432, 41, F4, 2, 24) (dual of [(41, 2), 50, 25]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(432, 41, F4, 3, 24) (dual of [(41, 3), 91, 25]-NRT-code) | [i] | ||
| 7 | No digital (8, 32, 41)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |