Information on Result #548014
There is no linear OA(918, 38, F9, 16) (dual of [38, 20, 17]-code), because construction Y1 would yield
- linear OA(917, 20, F9, 16) (dual of [20, 3, 17]-code), but
- linear OA(920, 38, F9, 18) (dual of [38, 18, 19]-code), but
- discarding factors / shortening the dual code would yield linear OA(920, 30, F9, 18) (dual of [30, 10, 19]-code), but
- residual code [i] would yield OA(92, 11, S9, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 89 > 92 [i]
- residual code [i] would yield OA(92, 11, S9, 2), but
- discarding factors / shortening the dual code would yield linear OA(920, 30, F9, 18) (dual of [30, 10, 19]-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(919, 39, F9, 17) (dual of [39, 20, 18]-code) | [i] | Truncation | |
| 2 | No linear OOA(919, 38, F9, 2, 17) (dual of [(38, 2), 57, 18]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(918, 38, F9, 2, 16) (dual of [(38, 2), 58, 17]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(918, 38, F9, 3, 16) (dual of [(38, 3), 96, 17]-NRT-code) | [i] | ||
| 5 | No digital (2, 18, 38)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |