Information on Result #2174732
There is no linear OA(246, 53, F2, 24) (dual of [53, 7, 25]-code), because 1 times code embedding in larger space would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- “vT4†bound on codes from Brouwer’s database [i]
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 OOA(247, 53, F2, 2, 25) (dual of [(53, 2), 59, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(246, 53, F2, 2, 24) (dual of [(53, 2), 60, 25]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(246, 53, F2, 3, 24) (dual of [(53, 3), 113, 25]-NRT-code) | [i] | ||
| 4 | No linear OOA(246, 53, F2, 4, 24) (dual of [(53, 4), 166, 25]-NRT-code) | [i] | ||
| 5 | No linear OOA(246, 53, F2, 5, 24) (dual of [(53, 5), 219, 25]-NRT-code) | [i] | ||
| 6 | No linear OOA(246, 53, F2, 6, 24) (dual of [(53, 6), 272, 25]-NRT-code) | [i] | ||
| 7 | No linear OOA(246, 53, F2, 7, 24) (dual of [(53, 7), 325, 25]-NRT-code) | [i] | ||
| 8 | No linear OOA(246, 53, F2, 8, 24) (dual of [(53, 8), 378, 25]-NRT-code) | [i] | ||
| 9 | No digital (22, 46, 53)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(294, 102, F2, 48) (dual of [102, 8, 49]-code) | [i] | Residual Code | |