Information on Result #548292
There is no linear OA(242, 63, F2, 20) (dual of [63, 21, 21]-code), because residual code would yield linear OA(222, 42, F2, 10) (dual of [42, 20, 11]-code), but
- adding a parity check bit [i] would yield linear OA(223, 43, F2, 11) (dual of [43, 20, 12]-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.
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(243, 64, F2, 21) (dual of [64, 21, 22]-code) | [i] | Truncation | |
| 2 | No linear OOA(243, 63, F2, 2, 21) (dual of [(63, 2), 83, 22]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(242, 63, F2, 2, 20) (dual of [(63, 2), 84, 21]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(242, 63, F2, 3, 20) (dual of [(63, 3), 147, 21]-NRT-code) | [i] | ||
| 5 | No linear OOA(242, 63, F2, 4, 20) (dual of [(63, 4), 210, 21]-NRT-code) | [i] | ||
| 6 | No linear OOA(242, 63, F2, 5, 20) (dual of [(63, 5), 273, 21]-NRT-code) | [i] | ||
| 7 | No linear OOA(242, 63, F2, 6, 20) (dual of [(63, 6), 336, 21]-NRT-code) | [i] | ||
| 8 | No linear OOA(242, 63, F2, 7, 20) (dual of [(63, 7), 399, 21]-NRT-code) | [i] | ||
| 9 | No linear OOA(242, 63, F2, 8, 20) (dual of [(63, 8), 462, 21]-NRT-code) | [i] | ||
| 10 | No digital (22, 42, 63)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |