Information on Result #560342
There is no linear OOA(4194, 208, F4, 2, 145) (dual of [(208, 2), 222, 146]-NRT-code), because 1 step m-reduction would yield linear OA(4193, 208, F4, 144) (dual of [208, 15, 145]-code), but
- construction Y1 [i] would yield
- linear OA(4192, 200, F4, 144) (dual of [200, 8, 145]-code), but
- construction Y1 [i] would yield
- linear OA(4191, 196, F4, 144) (dual of [196, 5, 145]-code), but
- residual code [i] would yield linear OA(447, 51, F4, 36) (dual of [51, 4, 37]-code), but
- OA(48, 200, S4, 4), but
- discarding factors would yield OA(48, 121, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 65704 > 48 [i]
- discarding factors would yield OA(48, 121, S4, 4), but
- linear OA(4191, 196, F4, 144) (dual of [196, 5, 145]-code), but
- construction Y1 [i] would yield
- OA(415, 208, S4, 8), but
- discarding factors would yield OA(415, 135, S4, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1082 768311 > 415 [i]
- discarding factors would yield OA(415, 135, S4, 8), but
- linear OA(4192, 200, F4, 144) (dual of [200, 8, 145]-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(4194, 208, F4, 3, 145) (dual of [(208, 3), 430, 146]-NRT-code) | [i] | Depth Reduction | |