Information on Result #547683
There is no linear OA(2120, 162, F2, 56) (dual of [162, 42, 57]-code), because construction Y1 would yield
- OA(2119, 146, S2, 56), but
- the linear programming bound shows that M ≥ 5165 551323 791927 774620 548045 364260 917630 468096 / 7704 797749 > 2119 [i]
- OA(242, 162, S2, 16), but
- discarding factors would yield OA(242, 146, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 467697 956730 > 242 [i]
- discarding factors would yield OA(242, 146, 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(2121, 163, F2, 57) (dual of [163, 42, 58]-code) | [i] | Truncation | |
| 2 | No linear OOA(2121, 162, F2, 2, 57) (dual of [(162, 2), 203, 58]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2120, 162, F2, 2, 56) (dual of [(162, 2), 204, 57]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2120, 162, F2, 3, 56) (dual of [(162, 3), 366, 57]-NRT-code) | [i] | ||
| 5 | No linear OOA(2120, 162, F2, 4, 56) (dual of [(162, 4), 528, 57]-NRT-code) | [i] | ||
| 6 | No linear OOA(2120, 162, F2, 5, 56) (dual of [(162, 5), 690, 57]-NRT-code) | [i] | ||
| 7 | No linear OOA(2120, 162, F2, 6, 56) (dual of [(162, 6), 852, 57]-NRT-code) | [i] | ||
| 8 | No linear OOA(2120, 162, F2, 7, 56) (dual of [(162, 7), 1014, 57]-NRT-code) | [i] | ||
| 9 | No linear OOA(2120, 162, F2, 8, 56) (dual of [(162, 8), 1176, 57]-NRT-code) | [i] | ||
| 10 | No digital (64, 120, 162)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2121, 190, F2, 56) (dual of [190, 69, 57]-code) | [i] | Construction Y1 (Bound) | |