Information on Result #547885
There is no linear OA(4159, 167, F4, 120) (dual of [167, 8, 121]-code), because construction Y1 would yield
- linear OA(4158, 163, F4, 120) (dual of [163, 5, 121]-code), but
- residual code [i] would yield linear OA(438, 42, F4, 30) (dual of [42, 4, 31]-code), but
- 2 times truncation [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- 2 times truncation [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(438, 42, F4, 30) (dual of [42, 4, 31]-code), but
- OA(48, 167, 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
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(4160, 175, F4, 120) (dual of [175, 15, 121]-code) | [i] | Construction Y1 (Bound) | |