Information on Result #548629
There is no linear OA(512, 17, F5, 10) (dual of [17, 5, 11]-code), because construction Y1 would yield
- OA(511, 13, S5, 10), but
- the (dual) Plotkin bound shows that M ≥ 732 421875 / 11 > 511 [i]
- linear OA(55, 17, F5, 4) (dual of [17, 12, 5]-code), but
- discarding factors / shortening the dual code would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-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 OOA(515, 17, F5, 2, 13) (dual of [(17, 2), 19, 14]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(516, 17, F5, 2, 14) (dual of [(17, 2), 18, 15]-NRT-code) | [i] | ||
| 3 | No linear OOA(517, 17, F5, 2, 15) (dual of [(17, 2), 17, 16]-NRT-code) | [i] | ||
| 4 | No linear OOA(512, 17, F5, 2, 10) (dual of [(17, 2), 22, 11]-NRT-code) | [i] | Depth Reduction | |
| 5 | No linear OOA(512, 17, F5, 3, 10) (dual of [(17, 3), 39, 11]-NRT-code) | [i] | ||
| 6 | No digital (2, 12, 17)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 7 | No linear OA(513, 37, F5, 10) (dual of [37, 24, 11]-code) | [i] | Construction Y1 (Bound) | |