Information on Result #1234958
Linear OOA(2169, 2098172, F2, 4, 12) (dual of [(2098172, 4), 8392519, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(231, 1022, F2, 4, 6) (dual of [(1022, 4), 4057, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (25, 31, 1022)-net over F2, using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F2, using
- extracting embedded OOA [i] based on digital (25, 31, 1022)-net over F2, using
- linear OOA(2138, 2097150, F2, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 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 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-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(2233, 4195322, F2, 4, 12) (dual of [(4195322, 4), 16781055, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |