Information on Result #548564
There is no linear OA(2196, 252, F2, 92) (dual of [252, 56, 93]-code), because construction Y1 would yield
- linear OA(2195, 232, F2, 92) (dual of [232, 37, 93]-code), but
- construction Y1 [i] would yield
- linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- adding a parity check bit [i] would yield linear OA(2195, 221, F2, 93) (dual of [221, 26, 94]-code), but
- OA(237, 232, S2, 12), but
- discarding factors would yield OA(237, 217, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 139173 045698 > 237 [i]
- discarding factors would yield OA(237, 217, S2, 12), but
- linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- construction Y1 [i] would yield
- OA(256, 252, S2, 20), but
- discarding factors would yield OA(256, 224, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 74952 904195 135741 > 256 [i]
- discarding factors would yield OA(256, 224, S2, 20), 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(2197, 253, F2, 93) (dual of [253, 56, 94]-code) | [i] | Truncation | |
| 2 | No linear OA(2198, 254, F2, 94) (dual of [254, 56, 95]-code) | [i] | ||
| 3 | No linear OA(2199, 255, F2, 95) (dual of [255, 56, 96]-code) | [i] | ||
| 4 | No linear OOA(2197, 252, F2, 2, 93) (dual of [(252, 2), 307, 94]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(2198, 252, F2, 2, 94) (dual of [(252, 2), 306, 95]-NRT-code) | [i] | ||
| 6 | No linear OOA(2199, 252, F2, 2, 95) (dual of [(252, 2), 305, 96]-NRT-code) | [i] | ||
| 7 | No linear OOA(2196, 252, F2, 2, 92) (dual of [(252, 2), 308, 93]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(2196, 252, F2, 3, 92) (dual of [(252, 3), 560, 93]-NRT-code) | [i] | ||
| 9 | No linear OOA(2196, 252, F2, 4, 92) (dual of [(252, 4), 812, 93]-NRT-code) | [i] | ||
| 10 | No linear OOA(2196, 252, F2, 5, 92) (dual of [(252, 5), 1064, 93]-NRT-code) | [i] | ||
| 11 | No linear OOA(2196, 252, F2, 6, 92) (dual of [(252, 6), 1316, 93]-NRT-code) | [i] | ||
| 12 | No linear OOA(2196, 252, F2, 7, 92) (dual of [(252, 7), 1568, 93]-NRT-code) | [i] | ||
| 13 | No linear OOA(2196, 252, F2, 8, 92) (dual of [(252, 8), 1820, 93]-NRT-code) | [i] | ||
| 14 | No digital (104, 196, 252)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |