Information on Result #548559
There is no linear OA(2183, 225, F2, 86) (dual of [225, 42, 87]-code), because construction Y1 would yield
- linear OA(2182, 211, F2, 86) (dual of [211, 29, 87]-code), but
- adding a parity check bit [i] would yield linear OA(2183, 212, F2, 87) (dual of [212, 29, 88]-code), but
- OA(242, 225, S2, 14), but
- discarding factors would yield OA(242, 219, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 498367 189624 > 242 [i]
- discarding factors would yield OA(242, 219, S2, 14), 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(2184, 226, F2, 87) (dual of [226, 42, 88]-code) | [i] | Truncation | |
| 2 | No linear OA(2185, 227, F2, 88) (dual of [227, 42, 89]-code) | [i] | ||
| 3 | No linear OA(2186, 228, F2, 89) (dual of [228, 42, 90]-code) | [i] | ||
| 4 | No linear OOA(2184, 225, F2, 2, 87) (dual of [(225, 2), 266, 88]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(2185, 225, F2, 2, 88) (dual of [(225, 2), 265, 89]-NRT-code) | [i] | ||
| 6 | No linear OOA(2186, 225, F2, 2, 89) (dual of [(225, 2), 264, 90]-NRT-code) | [i] | ||
| 7 | No linear OOA(2187, 225, F2, 2, 90) (dual of [(225, 2), 263, 91]-NRT-code) | [i] | ||
| 8 | No linear OOA(2188, 225, F2, 2, 91) (dual of [(225, 2), 262, 92]-NRT-code) | [i] | ||
| 9 | No linear OOA(2183, 225, F2, 2, 86) (dual of [(225, 2), 267, 87]-NRT-code) | [i] | Depth Reduction | |
| 10 | No linear OOA(2183, 225, F2, 3, 86) (dual of [(225, 3), 492, 87]-NRT-code) | [i] | ||
| 11 | No linear OOA(2183, 225, F2, 4, 86) (dual of [(225, 4), 717, 87]-NRT-code) | [i] | ||
| 12 | No linear OOA(2183, 225, F2, 5, 86) (dual of [(225, 5), 942, 87]-NRT-code) | [i] | ||
| 13 | No linear OOA(2183, 225, F2, 6, 86) (dual of [(225, 6), 1167, 87]-NRT-code) | [i] | ||
| 14 | No linear OOA(2183, 225, F2, 7, 86) (dual of [(225, 7), 1392, 87]-NRT-code) | [i] | ||
| 15 | No linear OOA(2183, 225, F2, 8, 86) (dual of [(225, 8), 1617, 87]-NRT-code) | [i] | ||
| 16 | No digital (97, 183, 225)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 17 | No linear OA(2184, 249, F2, 86) (dual of [249, 65, 87]-code) | [i] | Construction Y1 (Bound) | |