Information on Result #548650
There is no linear OA(914, 44, F9, 12) (dual of [44, 30, 13]-code), because construction Y1 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
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(915, 45, F9, 13) (dual of [45, 30, 14]-code) | [i] | Truncation | |
| 2 | No linear OA(916, 46, F9, 14) (dual of [46, 30, 15]-code) | [i] | ||
| 3 | No linear OA(917, 47, F9, 15) (dual of [47, 30, 16]-code) | [i] | ||
| 4 | No linear OOA(915, 44, F9, 2, 13) (dual of [(44, 2), 73, 14]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(916, 44, F9, 2, 14) (dual of [(44, 2), 72, 15]-NRT-code) | [i] | ||
| 6 | No linear OOA(917, 44, F9, 2, 15) (dual of [(44, 2), 71, 16]-NRT-code) | [i] | ||
| 7 | No linear OOA(914, 44, F9, 2, 12) (dual of [(44, 2), 74, 13]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(914, 44, F9, 3, 12) (dual of [(44, 3), 118, 13]-NRT-code) | [i] | ||
| 9 | No digital (2, 14, 44)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(936, 50, F9, 32) (dual of [50, 14, 33]-code) | [i] | Construction Y1 (Bound) | |