Information on Result #560019
There is no linear OOA(4167, 188, F4, 2, 125) (dual of [(188, 2), 209, 126]-NRT-code), because 1 step m-reduction would yield linear OA(4166, 188, F4, 124) (dual of [188, 22, 125]-code), but
- construction Y1 [i] would yield
- linear OA(4165, 176, F4, 124) (dual of [176, 11, 125]-code), but
- residual code [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- OA(422, 188, S4, 12), but
- discarding factors would yield OA(422, 164, S4, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 187369 733464 > 422 [i]
- discarding factors would yield OA(422, 164, S4, 12), but
- linear OA(4165, 176, F4, 124) (dual of [176, 11, 125]-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(4167, 188, F4, 3, 125) (dual of [(188, 3), 397, 126]-NRT-code) | [i] | Depth Reduction | |