Information on Result #2174748
There is no linear OA(2151, 178, F2, 72) (dual of [178, 27, 73]-code), because 1 times code embedding in larger space would yield linear OA(2152, 179, F2, 72) (dual of [179, 27, 73]-code), but
- adding a parity check bit [i] 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 OOA(2151, 178, F2, 2, 72) (dual of [(178, 2), 205, 73]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2151, 178, F2, 3, 72) (dual of [(178, 3), 383, 73]-NRT-code) | [i] | ||
| 3 | No linear OOA(2151, 178, F2, 4, 72) (dual of [(178, 4), 561, 73]-NRT-code) | [i] | ||
| 4 | No linear OOA(2151, 178, F2, 5, 72) (dual of [(178, 5), 739, 73]-NRT-code) | [i] | ||
| 5 | No linear OOA(2151, 178, F2, 6, 72) (dual of [(178, 6), 917, 73]-NRT-code) | [i] | ||
| 6 | No linear OOA(2151, 178, F2, 7, 72) (dual of [(178, 7), 1095, 73]-NRT-code) | [i] | ||
| 7 | No linear OOA(2151, 178, F2, 8, 72) (dual of [(178, 8), 1273, 73]-NRT-code) | [i] | ||