Information on Result #547770
There is no linear OA(3125, 176, F3, 79) (dual of [176, 51, 80]-code), because construction Y1 would yield
- OA(3124, 148, S3, 79), but
- the linear programming bound shows that M ≥ 690 317151 825090 850532 117017 983702 408086 595101 399831 232650 540048 412372 581649 / 3142 509791 861440 > 3124 [i]
- OA(351, 176, S3, 28), but
- discarding factors would yield OA(351, 172, S3, 28), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 263924 665338 043697 613937 > 351 [i]
- discarding factors would yield OA(351, 172, S3, 28), 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 OOA(3125, 176, F3, 2, 79) (dual of [(176, 2), 227, 80]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3125, 176, F3, 3, 79) (dual of [(176, 3), 403, 80]-NRT-code) | [i] | ||
| 3 | No linear OOA(3125, 176, F3, 4, 79) (dual of [(176, 4), 579, 80]-NRT-code) | [i] | ||
| 4 | No linear OOA(3125, 176, F3, 5, 79) (dual of [(176, 5), 755, 80]-NRT-code) | [i] | ||