Information on Result #1175282
Linear OOA(2109, 2097407, F2, 8, 9) (dual of [(2097407, 8), 16779147, 10]-NRT-code), using (u, u+v)-construction based on
- linear OOA(216, 257, F2, 8, 4) (dual of [(257, 8), 2040, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(216, 257, F2, 4, 4) (dual of [(257, 4), 1012, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(216, 257, F2, 3, 4) (dual of [(257, 3), 755, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 16, 257)-net over F2, using
- appending kth column [i] based on linear OOA(216, 257, F2, 3, 4) (dual of [(257, 3), 755, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(216, 257, F2, 4, 4) (dual of [(257, 4), 1012, 5]-NRT-code), using
- linear OOA(293, 2097150, F2, 8, 9) (dual of [(2097150, 8), 16777107, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-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(2109, 2097407, F2, 8, 8) (dual of [(2097407, 8), 16779147, 9]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2110, 2097407, F2, 8, 9) (dual of [(2097407, 8), 16779146, 10]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2109, 2097407, F2, 9, 9) (dual of [(2097407, 9), 18876554, 10]-NRT-code) | [i] | Appending kth Column | |