Information on Result #546442
There is no linear OA(2204, 245, F2, 98) (dual of [245, 41, 99]-code), because residual code would yield OA(2106, 146, S2, 49), but
- 1 times truncation [i] would yield OA(2105, 145, S2, 48), but
- the linear programming bound shows that M ≥ 727 070369 678229 731686 401086 929362 121333 407744 / 17 521374 765895 > 2105 [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(2205, 246, F2, 99) (dual of [246, 41, 100]-code) | [i] | Truncation | |
| 2 | No linear OOA(2205, 245, F2, 2, 99) (dual of [(245, 2), 285, 100]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2204, 245, F2, 2, 98) (dual of [(245, 2), 286, 99]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2204, 245, F2, 3, 98) (dual of [(245, 3), 531, 99]-NRT-code) | [i] | ||
| 5 | No linear OOA(2204, 245, F2, 4, 98) (dual of [(245, 4), 776, 99]-NRT-code) | [i] | ||
| 6 | No linear OOA(2204, 245, F2, 5, 98) (dual of [(245, 5), 1021, 99]-NRT-code) | [i] | ||
| 7 | No linear OOA(2204, 245, F2, 6, 98) (dual of [(245, 6), 1266, 99]-NRT-code) | [i] | ||
| 8 | No linear OOA(2204, 245, F2, 7, 98) (dual of [(245, 7), 1511, 99]-NRT-code) | [i] | ||
| 9 | No linear OOA(2204, 245, F2, 8, 98) (dual of [(245, 8), 1756, 99]-NRT-code) | [i] | ||
| 10 | No digital (106, 204, 245)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2205, 267, F2, 98) (dual of [267, 62, 99]-code) | [i] | Construction Y1 (Bound) | |