Information on Result #547684
There is no linear OA(2121, 190, F2, 56) (dual of [190, 69, 57]-code), because construction Y1 would yield
- linear OA(2120, 162, F2, 56) (dual of [162, 42, 57]-code), but
- construction Y1 [i] 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
- OA(2119, 146, S2, 56), but
- construction Y1 [i] would yield
- OA(269, 190, S2, 28), but
- the Rao or (dual) Hamming bound shows that M ≥ 608 937434 599922 686952 > 269 [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 OA(2122, 191, F2, 57) (dual of [191, 69, 58]-code) | [i] | Truncation | |
| 2 | No linear OOA(2122, 190, F2, 2, 57) (dual of [(190, 2), 258, 58]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2121, 190, F2, 2, 56) (dual of [(190, 2), 259, 57]-NRT-code) | [i] | Depth Reduction | |