Information on Result #2156261
There is no linear OA(2152, 179, F2, 72) (dual of [179, 27, 73]-code), because adding a parity check bit would yield linear OA(2153, 180, F2, 73) (dual of [180, 27, 74]-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(2152, 179, F2, 73) (dual of [179, 27, 74]-code) | [i] | Strength Reduction | |
| 2 | No linear OA(2151, 178, F2, 72) (dual of [178, 27, 73]-code) | [i] | Code Embedding in Larger Space | |
| 3 | No linear OA(2150, 177, F2, 72) (dual of [177, 27, 73]-code) | [i] | ||
| 4 | No linear OA(2149, 176, F2, 72) (dual of [176, 27, 73]-code) | [i] | ||
| 5 | No linear OOA(2153, 179, F2, 2, 73) (dual of [(179, 2), 205, 74]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(2152, 179, F2, 2, 72) (dual of [(179, 2), 206, 73]-NRT-code) | [i] | Depth Reduction | |
| 7 | No linear OOA(2152, 179, F2, 3, 72) (dual of [(179, 3), 385, 73]-NRT-code) | [i] | ||
| 8 | No linear OOA(2152, 179, F2, 4, 72) (dual of [(179, 4), 564, 73]-NRT-code) | [i] | ||
| 9 | No linear OOA(2152, 179, F2, 5, 72) (dual of [(179, 5), 743, 73]-NRT-code) | [i] | ||
| 10 | No linear OOA(2152, 179, F2, 6, 72) (dual of [(179, 6), 922, 73]-NRT-code) | [i] | ||
| 11 | No linear OOA(2152, 179, F2, 7, 72) (dual of [(179, 7), 1101, 73]-NRT-code) | [i] | ||
| 12 | No linear OOA(2152, 179, F2, 8, 72) (dual of [(179, 8), 1280, 73]-NRT-code) | [i] | ||
| 13 | No digital (80, 152, 179)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 14 | No linear OA(2153, 193, F2, 72) (dual of [193, 40, 73]-code) | [i] | Construction Y1 (Bound) | |