Information on Result #2174736
There is no linear OA(2109, 117, F2, 56) (dual of [117, 8, 57]-code), because 1 times code embedding in larger space would yield linear OA(2110, 118, F2, 56) (dual of [118, 8, 57]-code), but
- adding a parity check bit [i] would yield linear OA(2111, 119, F2, 57) (dual of [119, 8, 58]-code), but
- “DMa†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(2110, 117, F2, 2, 57) (dual of [(117, 2), 124, 58]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2109, 117, F2, 2, 56) (dual of [(117, 2), 125, 57]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2109, 117, F2, 3, 56) (dual of [(117, 3), 242, 57]-NRT-code) | [i] | ||
| 4 | No linear OOA(2109, 117, F2, 4, 56) (dual of [(117, 4), 359, 57]-NRT-code) | [i] | ||
| 5 | No linear OOA(2109, 117, F2, 5, 56) (dual of [(117, 5), 476, 57]-NRT-code) | [i] | ||
| 6 | No linear OOA(2109, 117, F2, 6, 56) (dual of [(117, 6), 593, 57]-NRT-code) | [i] | ||
| 7 | No linear OOA(2109, 117, F2, 7, 56) (dual of [(117, 7), 710, 57]-NRT-code) | [i] | ||
| 8 | No linear OOA(2109, 117, F2, 8, 56) (dual of [(117, 8), 827, 57]-NRT-code) | [i] | ||
| 9 | No digital (53, 109, 117)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(2221, 230, F2, 112) (dual of [230, 9, 113]-code) | [i] | Residual Code | |