Information on Result #546520
There is no linear OA(2243, 256, F2, 122) (dual of [256, 13, 123]-code), because residual code would yield OA(2121, 133, S2, 61), but
- 1 times truncation [i] would yield OA(2120, 132, S2, 60), but
- the linear programming bound shows that M ≥ 16503 694795 665515 477973 668460 440758 255616 / 10323 > 2120 [i]
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(2244, 257, F2, 123) (dual of [257, 13, 124]-code) | [i] | Truncation | |
| 2 | No linear OOA(2244, 256, F2, 2, 123) (dual of [(256, 2), 268, 124]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2243, 256, F2, 2, 122) (dual of [(256, 2), 269, 123]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2243, 256, F2, 3, 122) (dual of [(256, 3), 525, 123]-NRT-code) | [i] | ||
| 5 | No linear OOA(2243, 256, F2, 4, 122) (dual of [(256, 4), 781, 123]-NRT-code) | [i] | ||
| 6 | No linear OOA(2243, 256, F2, 5, 122) (dual of [(256, 5), 1037, 123]-NRT-code) | [i] | ||
| 7 | No linear OOA(2243, 256, F2, 6, 122) (dual of [(256, 6), 1293, 123]-NRT-code) | [i] | ||
| 8 | No linear OOA(2243, 256, F2, 7, 122) (dual of [(256, 7), 1549, 123]-NRT-code) | [i] | ||
| 9 | No linear OOA(2243, 256, F2, 8, 122) (dual of [(256, 8), 1805, 123]-NRT-code) | [i] | ||
| 10 | No digital (121, 243, 256)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |