Information on Result #551789
There is no linear OOA(2133, 185, F2, 2, 63) (dual of [(185, 2), 237, 64]-NRT-code), because 1 step m-reduction would yield linear OA(2132, 185, F2, 62) (dual of [185, 53, 63]-code), but
- construction Y1 [i] would yield
- linear OA(2131, 165, F2, 62) (dual of [165, 34, 63]-code), but
- construction Y1 [i] would yield
- linear OA(2130, 153, F2, 62) (dual of [153, 23, 63]-code), but
- adding a parity check bit [i] would yield linear OA(2131, 154, F2, 63) (dual of [154, 23, 64]-code), but
- OA(234, 165, S2, 12), but
- discarding factors would yield OA(234, 154, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 17486 314616 > 234 [i]
- discarding factors would yield OA(234, 154, S2, 12), but
- linear OA(2130, 153, F2, 62) (dual of [153, 23, 63]-code), but
- construction Y1 [i] would yield
- OA(253, 185, S2, 20), but
- discarding factors would yield OA(253, 182, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 9064 436853 738748 > 253 [i]
- discarding factors would yield OA(253, 182, S2, 20), but
- linear OA(2131, 165, F2, 62) (dual of [165, 34, 63]-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(2133, 185, F2, 3, 63) (dual of [(185, 3), 422, 64]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2133, 185, F2, 4, 63) (dual of [(185, 4), 607, 64]-NRT-code) | [i] | ||
| 3 | No linear OOA(2133, 185, F2, 5, 63) (dual of [(185, 5), 792, 64]-NRT-code) | [i] | ||
| 4 | No linear OOA(2133, 185, F2, 6, 63) (dual of [(185, 6), 977, 64]-NRT-code) | [i] | ||
| 5 | No linear OOA(2133, 185, F2, 7, 63) (dual of [(185, 7), 1162, 64]-NRT-code) | [i] | ||
| 6 | No linear OOA(2133, 185, F2, 8, 63) (dual of [(185, 8), 1347, 64]-NRT-code) | [i] | ||