Information on Result #547939
There is no linear OA(556, 65, F5, 45) (dual of [65, 9, 46]-code), because construction Y1 would yield
- linear OA(555, 59, F5, 45) (dual of [59, 4, 46]-code), but
- residual code [i] would yield linear OA(510, 13, F5, 9) (dual of [13, 3, 10]-code), but
- 1 times truncation [i] would yield linear OA(59, 12, F5, 8) (dual of [12, 3, 9]-code), but
- residual code [i] would yield linear OA(510, 13, F5, 9) (dual of [13, 3, 10]-code), but
- OA(59, 65, S5, 6), but
- discarding factors would yield OA(59, 58, S5, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 001465 > 59 [i]
- discarding factors would yield OA(59, 58, S5, 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 OOA(557, 65, F5, 2, 46) (dual of [(65, 2), 73, 47]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(558, 65, F5, 2, 47) (dual of [(65, 2), 72, 48]-NRT-code) | [i] | ||
| 3 | No linear OOA(556, 65, F5, 2, 45) (dual of [(65, 2), 74, 46]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(556, 65, F5, 3, 45) (dual of [(65, 3), 139, 46]-NRT-code) | [i] | ||
| 5 | No digital (11, 56, 65)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |