Information on Result #548542
There is no linear OA(2150, 194, F2, 70) (dual of [194, 44, 71]-code), because construction Y1 would yield
- linear OA(2149, 178, F2, 70) (dual of [178, 29, 71]-code), but
- adding a parity check bit [i] would yield linear OA(2150, 179, F2, 71) (dual of [179, 29, 72]-code), but
- OA(244, 194, S2, 16), but
- discarding factors would yield OA(244, 173, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 17 734855 699135 > 244 [i]
- discarding factors would yield OA(244, 173, S2, 16), 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(2151, 195, F2, 71) (dual of [195, 44, 72]-code) | [i] | Truncation | |
| 2 | No linear OOA(2151, 194, F2, 2, 71) (dual of [(194, 2), 237, 72]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2150, 194, F2, 2, 70) (dual of [(194, 2), 238, 71]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2150, 194, F2, 3, 70) (dual of [(194, 3), 432, 71]-NRT-code) | [i] | ||
| 5 | No linear OOA(2150, 194, F2, 4, 70) (dual of [(194, 4), 626, 71]-NRT-code) | [i] | ||
| 6 | No linear OOA(2150, 194, F2, 5, 70) (dual of [(194, 5), 820, 71]-NRT-code) | [i] | ||
| 7 | No linear OOA(2150, 194, F2, 6, 70) (dual of [(194, 6), 1014, 71]-NRT-code) | [i] | ||
| 8 | No linear OOA(2150, 194, F2, 7, 70) (dual of [(194, 7), 1208, 71]-NRT-code) | [i] | ||
| 9 | No linear OOA(2150, 194, F2, 8, 70) (dual of [(194, 8), 1402, 71]-NRT-code) | [i] | ||
| 10 | No digital (80, 150, 194)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2151, 222, F2, 70) (dual of [222, 71, 71]-code) | [i] | Construction Y1 (Bound) | |