Information on Result #548651
There is no linear OA(936, 50, F9, 32) (dual of [50, 14, 33]-code), because construction Y1 would yield
- linear OA(935, 38, F9, 32) (dual of [38, 3, 33]-code), but
- “Mas†bound on codes from Brouwer’s database [i]
- linear OA(914, 50, F9, 12) (dual of [50, 36, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(914, 44, F9, 12) (dual of [44, 30, 13]-code), but
- construction Y1 [i] would yield
- linear OA(913, 17, F9, 12) (dual of [17, 4, 13]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(930, 44, F9, 27) (dual of [44, 14, 28]-code), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- residual code [i] would yield OA(93, 11, S9, 3), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- linear OA(913, 17, F9, 12) (dual of [17, 4, 13]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(914, 44, F9, 12) (dual of [44, 30, 13]-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(937, 51, F9, 33) (dual of [51, 14, 34]-code) | [i] | Truncation | |
| 2 | No linear OA(938, 52, F9, 34) (dual of [52, 14, 35]-code) | [i] | ||
| 3 | No linear OA(939, 53, F9, 35) (dual of [53, 14, 36]-code) | [i] | ||
| 4 | No linear OOA(937, 50, F9, 2, 33) (dual of [(50, 2), 63, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(938, 50, F9, 2, 34) (dual of [(50, 2), 62, 35]-NRT-code) | [i] | ||
| 6 | No linear OOA(939, 50, F9, 2, 35) (dual of [(50, 2), 61, 36]-NRT-code) | [i] | ||
| 7 | No linear OOA(936, 50, F9, 2, 32) (dual of [(50, 2), 64, 33]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(936, 50, F9, 3, 32) (dual of [(50, 3), 114, 33]-NRT-code) | [i] | ||
| 9 | No digital (4, 36, 50)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(941, 77, F9, 36) (dual of [77, 36, 37]-code) | [i] | Construction Y1 (Bound) | |