Information on Result #1170706
Linear OOA(2100, 2097167, F2, 8, 8) (dual of [(2097167, 8), 16777236, 9]-NRT-code), using appending kth column based on linear OOA(2100, 2097167, F2, 7, 8) (dual of [(2097167, 7), 14680069, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(28, 17, F2, 7, 4) (dual of [(17, 7), 111, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(28, 17, F2, 4, 4) (dual of [(17, 4), 60, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(28, 17, F2, 3, 4) (dual of [(17, 3), 43, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 17)-net over F2, using
- appending kth column [i] based on linear OOA(28, 17, F2, 3, 4) (dual of [(17, 3), 43, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(28, 17, F2, 4, 4) (dual of [(17, 4), 60, 5]-NRT-code), using
- linear OOA(292, 2097150, F2, 7, 8) (dual of [(2097150, 7), 14679958, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(292, 8388600, F2, 8) (dual of [8388600, 8388508, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(292, 8388600, F2, 8) (dual of [8388600, 8388508, 9]-code), using
- linear OOA(28, 17, F2, 7, 4) (dual of [(17, 7), 111, 5]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (92, 100, 2097167)-net over F2 | [i] | Net Defined by OOA | |