Information on Result #2156266
There is no linear OA(2169, 197, F2, 80) (dual of [197, 28, 81]-code), because adding a parity check bit would yield linear OA(2170, 198, F2, 81) (dual of [198, 28, 82]-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(2169, 197, F2, 81) (dual of [197, 28, 82]-code) | [i] | Strength Reduction | |
| 2 | No linear OA(2168, 196, F2, 80) (dual of [196, 28, 81]-code) | [i] | Code Embedding in Larger Space | |
| 3 | No linear OA(2167, 195, F2, 80) (dual of [195, 28, 81]-code) | [i] | ||
| 4 | No linear OA(2166, 194, F2, 80) (dual of [194, 28, 81]-code) | [i] | ||
| 5 | No linear OOA(2170, 197, F2, 2, 81) (dual of [(197, 2), 224, 82]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(2169, 197, F2, 2, 80) (dual of [(197, 2), 225, 81]-NRT-code) | [i] | Depth Reduction | |
| 7 | No linear OOA(2169, 197, F2, 3, 80) (dual of [(197, 3), 422, 81]-NRT-code) | [i] | ||
| 8 | No linear OOA(2169, 197, F2, 4, 80) (dual of [(197, 4), 619, 81]-NRT-code) | [i] | ||
| 9 | No linear OOA(2169, 197, F2, 5, 80) (dual of [(197, 5), 816, 81]-NRT-code) | [i] | ||
| 10 | No linear OOA(2169, 197, F2, 6, 80) (dual of [(197, 6), 1013, 81]-NRT-code) | [i] | ||
| 11 | No linear OOA(2169, 197, F2, 7, 80) (dual of [(197, 7), 1210, 81]-NRT-code) | [i] | ||
| 12 | No linear OOA(2169, 197, F2, 8, 80) (dual of [(197, 8), 1407, 81]-NRT-code) | [i] | ||
| 13 | No digital (89, 169, 197)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 14 | No linear OA(2170, 211, F2, 80) (dual of [211, 41, 81]-code) | [i] | Construction Y1 (Bound) | |