Information on Result #547936
There is no linear OA(538, 61, F5, 30) (dual of [61, 23, 31]-code), because construction Y1 would yield
- linear OA(537, 43, F5, 30) (dual of [43, 6, 31]-code), but
- residual code [i] would yield linear OA(57, 12, F5, 6) (dual of [12, 5, 7]-code), but
- OA(523, 61, S5, 18), but
- the linear programming bound shows that M ≥ 6321 833259 448409 889221 191406 250000 / 502952 782605 714137 > 523 [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(539, 62, F5, 31) (dual of [62, 23, 32]-code) | [i] | Truncation | |
| 2 | No linear OOA(539, 61, F5, 2, 31) (dual of [(61, 2), 83, 32]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(538, 61, F5, 2, 30) (dual of [(61, 2), 84, 31]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(538, 61, F5, 3, 30) (dual of [(61, 3), 145, 31]-NRT-code) | [i] | ||
| 5 | No digital (8, 38, 61)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(526, 64, F5, 20) (dual of [64, 38, 21]-code) | [i] | Construction Y1 (Bound) | |