Information on Result #1175544
Linear OOA(2179, 1406291, F2, 8, 13) (dual of [(1406291, 8), 11250149, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(240, 8191, F2, 8, 6) (dual of [(8191, 8), 65488, 7]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(240, 8191, F2, 6, 6) (dual of [(8191, 6), 49106, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(240, 8191, F2, 5, 6) (dual of [(8191, 5), 40915, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- 1 times m-reduction [i] based on digital (34, 41, 8191)-net over F2, using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- appending kth column [i] based on linear OOA(240, 8191, F2, 5, 6) (dual of [(8191, 5), 40915, 7]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(240, 8191, F2, 6, 6) (dual of [(8191, 6), 49106, 7]-NRT-code), using
- linear OOA(2139, 1398100, F2, 8, 13) (dual of [(1398100, 8), 11184661, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 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 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-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(2179, 1406291, F2, 8, 12) (dual of [(1406291, 8), 11250149, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2180, 1406291, F2, 8, 13) (dual of [(1406291, 8), 11250148, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2181, 1406291, F2, 8, 13) (dual of [(1406291, 8), 11250147, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(2243, 2812582, F2, 8, 13) (dual of [(2812582, 8), 22500413, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |