Information on Result #2174744
There is no linear OA(2144, 172, F2, 70) (dual of [172, 28, 71]-code), because 4 times code embedding in larger space would yield linear OA(2148, 176, F2, 70) (dual of [176, 28, 71]-code), but
- adding a parity check bit [i] would yield linear OA(2149, 177, F2, 71) (dual of [177, 28, 72]-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 OOA(2145, 172, F2, 2, 71) (dual of [(172, 2), 199, 72]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(2144, 172, F2, 2, 70) (dual of [(172, 2), 200, 71]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(2144, 172, F2, 3, 70) (dual of [(172, 3), 372, 71]-NRT-code) | [i] | ||
| 4 | No linear OOA(2144, 172, F2, 4, 70) (dual of [(172, 4), 544, 71]-NRT-code) | [i] | ||
| 5 | No linear OOA(2144, 172, F2, 5, 70) (dual of [(172, 5), 716, 71]-NRT-code) | [i] | ||
| 6 | No linear OOA(2144, 172, F2, 6, 70) (dual of [(172, 6), 888, 71]-NRT-code) | [i] | ||
| 7 | No linear OOA(2144, 172, F2, 7, 70) (dual of [(172, 7), 1060, 71]-NRT-code) | [i] | ||
| 8 | No linear OOA(2144, 172, F2, 8, 70) (dual of [(172, 8), 1232, 71]-NRT-code) | [i] | ||
| 9 | No digital (74, 144, 172)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |