Information on Result #547089
There is no linear OA(410, 15, F4, 8) (dual of [15, 5, 9]-code), because residual code would yield OA(42, 6, S4, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 19 > 42 [i]
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(411, 16, F4, 9) (dual of [16, 5, 10]-code) | [i] | Truncation | |
| 2 | No linear OA(412, 17, F4, 10) (dual of [17, 5, 11]-code) | [i] | ||
| 3 | No linear OOA(411, 15, F4, 2, 9) (dual of [(15, 2), 19, 10]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(412, 15, F4, 2, 10) (dual of [(15, 2), 18, 11]-NRT-code) | [i] | ||
| 5 | No linear OOA(410, 15, F4, 2, 8) (dual of [(15, 2), 20, 9]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(410, 15, F4, 3, 8) (dual of [(15, 3), 35, 9]-NRT-code) | [i] | ||
| 7 | No digital (2, 10, 15)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 8 | No linear OA(442, 48, F4, 32) (dual of [48, 6, 33]-code) | [i] | Residual Code | |
| 9 | No linear OA(48, 18, F4, 6) (dual of [18, 10, 7]-code) | [i] | Construction Y1 (Bound) | |
| 10 | No linear OA(411, 29, F4, 8) (dual of [29, 18, 9]-code) | [i] | ||