Information on Result #548461
There is no linear OA(3165, 171, F3, 111) (dual of [171, 6, 112]-code), because residual code would yield linear OA(354, 59, F3, 37) (dual of [59, 5, 38]-code), but
- 1 times truncation [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- residual code [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-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(3166, 172, F3, 112) (dual of [172, 6, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3167, 173, F3, 113) (dual of [173, 6, 114]-code) | [i] | ||
| 3 | No linear OOA(3165, 171, F3, 2, 111) (dual of [(171, 2), 177, 112]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(3165, 171, F3, 3, 111) (dual of [(171, 3), 348, 112]-NRT-code) | [i] | ||
| 5 | No linear OOA(3165, 171, F3, 4, 111) (dual of [(171, 4), 519, 112]-NRT-code) | [i] | ||
| 6 | No linear OOA(3165, 171, F3, 5, 111) (dual of [(171, 5), 690, 112]-NRT-code) | [i] | ||
| 7 | No linear OA(3166, 175, F3, 111) (dual of [175, 9, 112]-code) | [i] | Construction Y1 (Bound) | |