Information on Result #548353
There is no linear OA(2163, 174, F2, 82) (dual of [174, 11, 83]-code), because residual code would yield linear OA(281, 91, F2, 41) (dual of [91, 10, 42]-code), but
- 1 times truncation [i] would yield linear OA(280, 90, F2, 40) (dual of [90, 10, 41]-code), but
- residual code [i] would yield linear OA(240, 49, F2, 20) (dual of [49, 9, 21]-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(2164, 175, F2, 83) (dual of [175, 11, 84]-code) | [i] | Truncation | |
| 2 | No linear OOA(2164, 174, F2, 2, 83) (dual of [(174, 2), 184, 84]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2163, 174, F2, 2, 82) (dual of [(174, 2), 185, 83]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2163, 174, F2, 3, 82) (dual of [(174, 3), 359, 83]-NRT-code) | [i] | ||
| 5 | No linear OOA(2163, 174, F2, 4, 82) (dual of [(174, 4), 533, 83]-NRT-code) | [i] | ||
| 6 | No linear OOA(2163, 174, F2, 5, 82) (dual of [(174, 5), 707, 83]-NRT-code) | [i] | ||
| 7 | No linear OOA(2163, 174, F2, 6, 82) (dual of [(174, 6), 881, 83]-NRT-code) | [i] | ||
| 8 | No linear OOA(2163, 174, F2, 7, 82) (dual of [(174, 7), 1055, 83]-NRT-code) | [i] | ||
| 9 | No linear OOA(2163, 174, F2, 8, 82) (dual of [(174, 8), 1229, 83]-NRT-code) | [i] | ||
| 10 | No digital (81, 163, 174)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |