Information on Result #1684896
Linear OOA(2197, 2099197, F2, 7, 15) (dual of [(2099197, 7), 14694182, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2197, 2099197, F2, 4, 15) (dual of [(2099197, 4), 8396591, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(235, 2047, F2, 4, 7) (dual of [(2047, 4), 8153, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 35, 2047)-net over F2, using
- linear OOA(2162, 2097150, F2, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 4-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- linear OOA(235, 2047, F2, 4, 7) (dual of [(2047, 4), 8153, 8]-NRT-code), using
Mode: 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(2198, 2099197, F2, 7, 15) (dual of [(2099197, 7), 14694181, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2197, 2099196, F2, 8, 15) (dual of [(2099196, 8), 16793371, 16]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 3 | Linear OOA(2197, 2099196, F2, 21, 15) (dual of [(2099196, 21), 44082919, 16]-NRT-code) | [i] | ||