Information on Result #552237
There is no linear OOA(2154, 193, F2, 2, 73) (dual of [(193, 2), 232, 74]-NRT-code), because 1 step m-reduction would yield linear OA(2153, 193, F2, 72) (dual of [193, 40, 73]-code), but
- construction Y1 [i] 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
- OA(240, 193, S2, 14), but
- discarding factors would yield OA(240, 180, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 124371 299892 > 240 [i]
- discarding factors would yield OA(240, 180, S2, 14), but
- linear OA(2152, 179, F2, 72) (dual of [179, 27, 73]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(2154, 193, F2, 3, 73) (dual of [(193, 3), 425, 74]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2154, 193, F2, 4, 73) (dual of [(193, 4), 618, 74]-NRT-code) | [i] | ||
| 3 | No linear OOA(2154, 193, F2, 5, 73) (dual of [(193, 5), 811, 74]-NRT-code) | [i] | ||
| 4 | No linear OOA(2154, 193, F2, 6, 73) (dual of [(193, 6), 1004, 74]-NRT-code) | [i] | ||
| 5 | No linear OOA(2154, 193, F2, 7, 73) (dual of [(193, 7), 1197, 74]-NRT-code) | [i] | ||
| 6 | No linear OOA(2154, 193, F2, 8, 73) (dual of [(193, 8), 1390, 74]-NRT-code) | [i] | ||