Information on Result #1159320
Linear OOA(2104, 2097215, F2, 7, 8) (dual of [(2097215, 7), 14680401, 9]-NRT-code), using (u, u+v)-construction based on
- linear OOA(212, 65, F2, 7, 4) (dual of [(65, 7), 443, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(212, 65, F2, 4, 4) (dual of [(65, 4), 248, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(212, 65, F2, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 12, 65)-net over F2, using
- appending kth column [i] based on linear OOA(212, 65, F2, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(212, 65, F2, 4, 4) (dual of [(65, 4), 248, 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
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 | Linear OOA(2104, 2097215, F2, 8, 8) (dual of [(2097215, 8), 16777616, 9]-NRT-code) | [i] | Appending kth Column | |