Information on Result #1205898
Digital (187, 199, 2446674)-net over F2, using (u, u+v)-construction based on
- digital (55, 61, 1048574)-net over F2, using
- 1 times m-reduction [i] based on digital (55, 62, 1048574)-net over F2, using
- net defined by OOA [i] based on linear OOA(262, 1048574, F2, 7, 7) (dual of [(1048574, 7), 7339956, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(262, 1048575, F2, 3, 7) (dual of [(1048575, 3), 3145663, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(262, 1048574, F2, 7, 7) (dual of [(1048574, 7), 7339956, 8]-NRT-code), using
- 1 times m-reduction [i] based on digital (55, 62, 1048574)-net over F2, using
- digital (126, 138, 1398100)-net over F2, using
- net defined by OOA [i] based on linear OOA(2138, 1398100, F2, 12, 12) (dual of [(1398100, 12), 16777062, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- net defined by OOA [i] based on linear OOA(2138, 1398100, F2, 12, 12) (dual of [(1398100, 12), 16777062, 13]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2199, 2446674, F2, 6, 12) (dual of [(2446674, 6), 14679845, 13]-NRT-code) | [i] | Extracting Embedded OOA | |
| 2 | Linear OOA(2199, 2446674, F2, 7, 12) (dual of [(2446674, 7), 17126519, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2199, 2446674, F2, 8, 12) (dual of [(2446674, 8), 19573193, 13]-NRT-code) | [i] | ||