Information on Result #559979
There is no linear OOA(4162, 172, F4, 2, 122) (dual of [(172, 2), 182, 123]-NRT-code), because 2 step m-reduction would yield linear OA(4160, 172, F4, 120) (dual of [172, 12, 121]-code), but
- construction Y1 [i] 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
- linear OA(4159, 166, F4, 120) (dual of [166, 7, 121]-code), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(4162, 172, F4, 3, 122) (dual of [(172, 3), 354, 123]-NRT-code) | [i] | Depth Reduction | |