Information on Result #547824
There is no linear OA(415, 19, F4, 12) (dual of [19, 4, 13]-code), because construction Y1 would yield
- OA(414, 16, S4, 12), but
- the (dual) Plotkin bound shows that M ≥ 4294 967296 / 13 > 414 [i]
- linear OA(44, 19, F4, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,4)), but
- discarding factors / shortening the dual code would yield linear OA(44, 18, F4, 3) (dual of [18, 14, 4]-code or 18-cap in PG(3,4)), 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(416, 20, F4, 13) (dual of [20, 4, 14]-code) | [i] | Truncation | |
| 2 | No linear OA(417, 21, F4, 14) (dual of [21, 4, 15]-code) | [i] | ||
| 3 | No linear OA(418, 22, F4, 15) (dual of [22, 4, 16]-code) | [i] | ||
| 4 | No linear OA(416, 29, F4, 12) (dual of [29, 13, 13]-code) | [i] | Construction Y1 (Bound) | |