Information on Result #548049
There is no linear OA(2550, 102, F25, 48) (dual of [102, 52, 49]-code), because construction Y1 would yield
- linear OA(2549, 52, F25, 48) (dual of [52, 3, 49]-code), but
- linear OA(2552, 102, F25, 50) (dual of [102, 50, 51]-code), but
- discarding factors / shortening the dual code would yield linear OA(2552, 78, F25, 50) (dual of [78, 26, 51]-code), but
- residual code [i] would yield OA(252, 27, S25, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 649 > 252 [i]
- residual code [i] would yield OA(252, 27, S25, 2), but
- discarding factors / shortening the dual code would yield linear OA(2552, 78, F25, 50) (dual of [78, 26, 51]-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(2551, 103, F25, 49) (dual of [103, 52, 50]-code) | [i] | Truncation | |
| 2 | No linear OOA(2551, 102, F25, 2, 49) (dual of [(102, 2), 153, 50]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2550, 102, F25, 2, 48) (dual of [(102, 2), 154, 49]-NRT-code) | [i] | Depth Reduction | |
| 4 | No digital (2, 50, 102)-net over F25 | [i] | Extracting Embedded Orthogonal Array | |