Information on Result #1685321
Linear OOA(2203, 2105341, F2, 7, 15) (dual of [(2105341, 7), 14737184, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2203, 2105341, F2, 4, 15) (dual of [(2105341, 4), 8421161, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(241, 8191, F2, 4, 7) (dual of [(8191, 4), 32723, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 41, 8191)-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(241, 8191, F2, 4, 7) (dual of [(8191, 4), 32723, 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(2204, 2105341, F2, 7, 15) (dual of [(2105341, 7), 14737183, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2203, 2105340, F2, 8, 15) (dual of [(2105340, 8), 16842517, 16]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 3 | Linear OOA(2203, 2105340, F2, 21, 15) (dual of [(2105340, 21), 44211937, 16]-NRT-code) | [i] | ||