Information on Result #1683993
Linear OOA(2184, 2097277, F2, 7, 14) (dual of [(2097277, 7), 14680755, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2184, 2097277, F2, 4, 14) (dual of [(2097277, 4), 8388924, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(223, 127, F2, 4, 7) (dual of [(127, 4), 485, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 23, 127)-net over F2, using
- linear OOA(2161, 2097150, F2, 4, 14) (dual of [(2097150, 4), 8388439, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OOA 4-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-code), using
- linear OOA(223, 127, F2, 4, 7) (dual of [(127, 4), 485, 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(2185, 2097277, F2, 7, 14) (dual of [(2097277, 7), 14680754, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2184, 2097276, F2, 8, 14) (dual of [(2097276, 8), 16778024, 15]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 3 | Linear OOA(2184, 2097276, F2, 21, 14) (dual of [(2097276, 21), 44042612, 15]-NRT-code) | [i] | ||