Information on Result #548312
There is no linear OA(2113, 127, F2, 56) (dual of [127, 14, 57]-code), because residual code would yield linear OA(257, 70, F2, 28) (dual of [70, 13, 29]-code), but
- adding a parity check bit [i] would yield linear OA(258, 71, F2, 29) (dual of [71, 13, 30]-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(2114, 128, F2, 57) (dual of [128, 14, 58]-code) | [i] | Truncation | |
| 2 | No linear OOA(2114, 127, F2, 2, 57) (dual of [(127, 2), 140, 58]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2113, 127, F2, 2, 56) (dual of [(127, 2), 141, 57]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2113, 127, F2, 3, 56) (dual of [(127, 3), 268, 57]-NRT-code) | [i] | ||
| 5 | No linear OOA(2113, 127, F2, 4, 56) (dual of [(127, 4), 395, 57]-NRT-code) | [i] | ||
| 6 | No linear OOA(2113, 127, F2, 5, 56) (dual of [(127, 5), 522, 57]-NRT-code) | [i] | ||
| 7 | No linear OOA(2113, 127, F2, 6, 56) (dual of [(127, 6), 649, 57]-NRT-code) | [i] | ||
| 8 | No linear OOA(2113, 127, F2, 7, 56) (dual of [(127, 7), 776, 57]-NRT-code) | [i] | ||
| 9 | No linear OOA(2113, 127, F2, 8, 56) (dual of [(127, 8), 903, 57]-NRT-code) | [i] | ||
| 10 | No digital (57, 113, 127)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2225, 240, F2, 112) (dual of [240, 15, 113]-code) | [i] | Residual Code | |