Information on Result #548612
There is no linear OA(416, 29, F4, 12) (dual of [29, 13, 13]-code), because construction Y1 would yield
- linear OA(415, 19, F4, 12) (dual of [19, 4, 13]-code), but
- construction Y1 [i] 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
- OA(414, 16, S4, 12), but
- construction Y1 [i] would yield
- linear OA(413, 29, F4, 10) (dual of [29, 16, 11]-code), but
- discarding factors / shortening the dual code would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-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.
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(417, 30, F4, 13) (dual of [30, 13, 14]-code) | [i] | Truncation | |
| 2 | No linear OOA(417, 29, F4, 2, 13) (dual of [(29, 2), 41, 14]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(416, 29, F4, 2, 12) (dual of [(29, 2), 42, 13]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(416, 29, F4, 3, 12) (dual of [(29, 3), 71, 13]-NRT-code) | [i] | ||
| 5 | No digital (4, 16, 29)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(414, 30, F4, 10) (dual of [30, 16, 11]-code) | [i] | Construction Y1 (Bound) | |