Information on Result #548054
There is no linear OA(2754, 110, F27, 52) (dual of [110, 56, 53]-code), because construction Y1 would yield
- linear OA(2753, 56, F27, 52) (dual of [56, 3, 53]-code), but
- linear OA(2756, 110, F27, 54) (dual of [110, 54, 55]-code), but
- discarding factors / shortening the dual code would yield linear OA(2756, 84, F27, 54) (dual of [84, 28, 55]-code), but
- residual code [i] would yield OA(272, 29, S27, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 755 > 272 [i]
- residual code [i] would yield OA(272, 29, S27, 2), but
- discarding factors / shortening the dual code would yield linear OA(2756, 84, F27, 54) (dual of [84, 28, 55]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2755, 111, F27, 53) (dual of [111, 56, 54]-code) | [i] | Truncation | |
| 2 | No linear OOA(2755, 110, F27, 2, 53) (dual of [(110, 2), 165, 54]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2754, 110, F27, 2, 52) (dual of [(110, 2), 166, 53]-NRT-code) | [i] | Depth Reduction | |
| 4 | No digital (2, 54, 110)-net over F27 | [i] | Extracting Embedded Orthogonal Array | |