Information on Result #548639
There is no linear OA(728, 40, F7, 24) (dual of [40, 12, 25]-code), because construction Y1 would yield
- linear OA(727, 30, F7, 24) (dual of [30, 3, 25]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(712, 40, F7, 10) (dual of [40, 28, 11]-code), but
- discarding factors / shortening the dual code would yield linear OA(712, 36, F7, 10) (dual of [36, 24, 11]-code), but
- construction Y1 [i] would yield
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-code), but
- “BPM†bound on codes from Brouwer’s database [i]
- linear OA(724, 36, F7, 21) (dual of [36, 12, 22]-code), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- residual code [i] would yield OA(73, 9, S7, 3), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(712, 36, F7, 10) (dual of [36, 24, 11]-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(729, 41, F7, 25) (dual of [41, 12, 26]-code) | [i] | Truncation | |
| 2 | No linear OA(730, 42, F7, 26) (dual of [42, 12, 27]-code) | [i] | ||
| 3 | No linear OA(731, 43, F7, 27) (dual of [43, 12, 28]-code) | [i] | ||
| 4 | No linear OOA(729, 40, F7, 2, 25) (dual of [(40, 2), 51, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(730, 40, F7, 2, 26) (dual of [(40, 2), 50, 27]-NRT-code) | [i] | ||
| 6 | No linear OOA(731, 40, F7, 2, 27) (dual of [(40, 2), 49, 28]-NRT-code) | [i] | ||
| 7 | No linear OOA(728, 40, F7, 2, 24) (dual of [(40, 2), 52, 25]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(728, 40, F7, 3, 24) (dual of [(40, 3), 92, 25]-NRT-code) | [i] | ||
| 9 | No digital (4, 28, 40)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(725, 53, F7, 21) (dual of [53, 28, 22]-code) | [i] | Construction Y1 (Bound) | |