Information on Result #1234972
Linear OOA(2189, 2162685, F2, 4, 12) (dual of [(2162685, 4), 8650551, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(249, 65534, F2, 4, 6) (dual of [(65534, 4), 262087, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (43, 49, 65534)-net over F2, using
- 1 times m-reduction [i] based on digital (43, 50, 65534)-net over F2, using
- net defined by OOA [i] based on linear OOA(250, 65534, F2, 7, 7) (dual of [(65534, 7), 458688, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(250, 65535, F2, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(250, 65534, F2, 7, 7) (dual of [(65534, 7), 458688, 8]-NRT-code), using
- 1 times m-reduction [i] based on digital (43, 50, 65534)-net over F2, using
- extracting embedded OOA [i] based on digital (43, 49, 65534)-net over F2, using
- linear OOA(2140, 2097151, F2, 4, 12) (dual of [(2097151, 4), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2140, 4194302, F2, 2, 12) (dual of [(4194302, 2), 8388464, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2138, 4194301, F2, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2138, 4194301, F2, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2140, 4194302, F2, 2, 12) (dual of [(4194302, 2), 8388464, 13]-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 | Linear OOA(2253, 4259835, F2, 4, 12) (dual of [(4259835, 4), 17039087, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |