Information on Result #548544
There is no linear OA(2153, 193, F2, 72) (dual of [193, 40, 73]-code), because construction Y1 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
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(2154, 194, F2, 73) (dual of [194, 40, 74]-code) | [i] | Truncation | |
| 2 | No linear OOA(2154, 193, F2, 2, 73) (dual of [(193, 2), 232, 74]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2153, 193, F2, 2, 72) (dual of [(193, 2), 233, 73]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2153, 193, F2, 3, 72) (dual of [(193, 3), 426, 73]-NRT-code) | [i] | ||
| 5 | No linear OOA(2153, 193, F2, 4, 72) (dual of [(193, 4), 619, 73]-NRT-code) | [i] | ||
| 6 | No linear OOA(2153, 193, F2, 5, 72) (dual of [(193, 5), 812, 73]-NRT-code) | [i] | ||
| 7 | No linear OOA(2153, 193, F2, 6, 72) (dual of [(193, 6), 1005, 73]-NRT-code) | [i] | ||
| 8 | No linear OOA(2153, 193, F2, 7, 72) (dual of [(193, 7), 1198, 73]-NRT-code) | [i] | ||
| 9 | No linear OOA(2153, 193, F2, 8, 72) (dual of [(193, 8), 1391, 73]-NRT-code) | [i] | ||
| 10 | No digital (81, 153, 193)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |