Information on Result #548618
There is no linear OA(4160, 172, F4, 120) (dual of [172, 12, 121]-code), because construction Y1 would yield
- linear OA(4159, 166, F4, 120) (dual of [166, 7, 121]-code), but
- residual code [i] would yield linear OA(439, 45, F4, 30) (dual of [45, 6, 31]-code), but
- OA(412, 172, S4, 6), but
- discarding factors would yield OA(412, 156, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 16 866019 > 412 [i]
- discarding factors would yield OA(412, 156, 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(4161, 173, F4, 121) (dual of [173, 12, 122]-code) | [i] | Truncation | |
| 2 | No linear OA(4162, 174, F4, 122) (dual of [174, 12, 123]-code) | [i] | ||
| 3 | No linear OA(4163, 175, F4, 123) (dual of [175, 12, 124]-code) | [i] | ||
| 4 | No linear OOA(4161, 172, F4, 2, 121) (dual of [(172, 2), 183, 122]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4162, 172, F4, 2, 122) (dual of [(172, 2), 182, 123]-NRT-code) | [i] | ||
| 6 | No linear OOA(4163, 172, F4, 2, 123) (dual of [(172, 2), 181, 124]-NRT-code) | [i] | ||
| 7 | No linear OOA(4160, 172, F4, 2, 120) (dual of [(172, 2), 184, 121]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4160, 172, F4, 3, 120) (dual of [(172, 3), 356, 121]-NRT-code) | [i] | ||
| 9 | No digital (40, 160, 172)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(4161, 186, F4, 120) (dual of [186, 25, 121]-code) | [i] | Construction Y1 (Bound) | |