Information on Result #1235011
Linear OOA(2172, 2098173, F2, 4, 13) (dual of [(2098173, 4), 8392520, 14]-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(2141, 2097151, F2, 4, 13) (dual of [(2097151, 4), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2141, 4194302, F2, 2, 13) (dual of [(4194302, 2), 8388463, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2141, 4194302, F2, 2, 13) (dual of [(4194302, 2), 8388463, 14]-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(2236, 4195323, F2, 4, 13) (dual of [(4195323, 4), 16781056, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |