Information on Result #548628
There is no linear OA(57, 42, F5, 5) (dual of [42, 35, 6]-code), because construction Y1 would yield
- linear OA(56, 13, F5, 5) (dual of [13, 7, 6]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(57, 13, F5, 6) (dual of [13, 6, 7]-code), but
- discarding factors / shortening the dual code would yield linear OA(57, 12, F5, 6) (dual of [12, 5, 7]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(57, 13, F5, 6) (dual of [13, 6, 7]-code), but
- linear OA(535, 42, F5, 29) (dual of [42, 7, 30]-code), but
- discarding factors / shortening the dual code would yield linear OA(535, 41, F5, 29) (dual of [41, 6, 30]-code), but
- “DG1†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(535, 41, F5, 29) (dual of [41, 6, 30]-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(57, 42, F5, 2, 5) (dual of [(42, 2), 77, 6]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(57, 42, F5, 3, 5) (dual of [(42, 3), 119, 6]-NRT-code) | [i] | ||
| 3 | No digital (2, 7, 42)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |