Information on Result #548358
There is no linear OA(2167, 178, F2, 84) (dual of [178, 11, 85]-code), because residual code would yield linear OA(283, 93, F2, 42) (dual of [93, 10, 43]-code), but
- residual code [i] would yield linear OA(241, 50, F2, 21) (dual of [50, 9, 22]-code), but
- 1 times truncation [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(2168, 179, F2, 85) (dual of [179, 11, 86]-code) | [i] | Truncation | |
| 2 | No linear OOA(2168, 178, F2, 2, 85) (dual of [(178, 2), 188, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2170, 178, F2, 2, 87) (dual of [(178, 2), 186, 88]-NRT-code) | [i] | ||
| 4 | No linear OOA(2167, 178, F2, 2, 84) (dual of [(178, 2), 189, 85]-NRT-code) | [i] | Depth Reduction | |
| 5 | No linear OOA(2167, 178, F2, 3, 84) (dual of [(178, 3), 367, 85]-NRT-code) | [i] | ||
| 6 | No linear OOA(2167, 178, F2, 4, 84) (dual of [(178, 4), 545, 85]-NRT-code) | [i] | ||
| 7 | No linear OOA(2167, 178, F2, 5, 84) (dual of [(178, 5), 723, 85]-NRT-code) | [i] | ||
| 8 | No linear OOA(2167, 178, F2, 6, 84) (dual of [(178, 6), 901, 85]-NRT-code) | [i] | ||
| 9 | No linear OOA(2167, 178, F2, 7, 84) (dual of [(178, 7), 1079, 85]-NRT-code) | [i] | ||
| 10 | No linear OOA(2167, 178, F2, 8, 84) (dual of [(178, 8), 1257, 85]-NRT-code) | [i] | ||
| 11 | No digital (83, 167, 178)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |