Information on Result #547932
There is no linear OA(519, 42, F5, 15) (dual of [42, 23, 16]-code), because construction Y1 would yield
- linear OA(518, 23, F5, 15) (dual of [23, 5, 16]-code), but
- residual code [i] would yield OA(53, 7, S5, 3), but
- OA(523, 42, S5, 19), but
- discarding factors would yield OA(523, 41, S5, 19), but
- the linear programming bound shows that M ≥ 1431 381081 044673 919677 734375 / 117616 346784 > 523 [i]
- discarding factors would yield OA(523, 41, S5, 19), 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(520, 43, F5, 16) (dual of [43, 23, 17]-code) | [i] | Truncation | |
| 2 | No linear OA(521, 44, F5, 17) (dual of [44, 23, 18]-code) | [i] | ||
| 3 | No linear OOA(520, 42, F5, 2, 16) (dual of [(42, 2), 64, 17]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(521, 42, F5, 2, 17) (dual of [(42, 2), 63, 18]-NRT-code) | [i] | ||
| 5 | No linear OOA(522, 42, F5, 2, 18) (dual of [(42, 2), 62, 19]-NRT-code) | [i] | ||
| 6 | No linear OOA(519, 42, F5, 2, 15) (dual of [(42, 2), 65, 16]-NRT-code) | [i] | Depth Reduction | |
| 7 | No linear OOA(519, 42, F5, 3, 15) (dual of [(42, 3), 107, 16]-NRT-code) | [i] | ||
| 8 | No digital (4, 19, 42)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |