Information on Result #1175682
Linear OOA(2183, 1198435, F2, 8, 15) (dual of [(1198435, 8), 9587297, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(221, 64, F2, 8, 7) (dual of [(64, 8), 491, 8]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(221, 64, F2, 7, 7) (dual of [(64, 7), 427, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(221, 64, F2, 6, 7) (dual of [(64, 6), 363, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 21, 64)-net over F2, using
- appending kth column [i] based on linear OOA(221, 64, F2, 6, 7) (dual of [(64, 6), 363, 8]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(221, 64, F2, 7, 7) (dual of [(64, 7), 427, 8]-NRT-code), using
- linear OOA(2162, 1198371, F2, 8, 15) (dual of [(1198371, 8), 9586806, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-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(2183, 1198435, F2, 8, 14) (dual of [(1198435, 8), 9587297, 15]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2184, 1198435, F2, 8, 15) (dual of [(1198435, 8), 9587296, 16]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2248, 2396870, F2, 8, 15) (dual of [(2396870, 8), 19174712, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |