Information on Result #548636
There is no linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), because construction Y1 would yield
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(732, 42, F7, 28) (dual of [42, 10, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(732, 38, F7, 28) (dual of [38, 6, 29]-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 OA(711, 43, F7, 9) (dual of [43, 32, 10]-code) | [i] | Truncation | |
| 2 | No linear OOA(711, 42, F7, 2, 9) (dual of [(42, 2), 73, 10]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(710, 42, F7, 2, 8) (dual of [(42, 2), 74, 9]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(710, 42, F7, 3, 8) (dual of [(42, 3), 116, 9]-NRT-code) | [i] | ||
| 5 | No digital (2, 10, 42)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(735, 45, F7, 30) (dual of [45, 10, 31]-code) | [i] | Construction Y1 (Bound) | |