Information on Result #1193264
Digital (43, 52, 265724)-net over F9, using net defined by OOA based on linear OOA(952, 265724, F9, 9, 9) (dual of [(265724, 9), 2391464, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(952, 1062897, F9, 9) (dual of [1062897, 1062845, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(952, 1062898, F9, 9) (dual of [1062898, 1062846, 10]-code), using
- trace code [i] based on linear OA(8126, 531449, F81, 9) (dual of [531449, 531423, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(8125, 531442, F81, 9) (dual of [531442, 531417, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(8119, 531442, F81, 7) (dual of [531442, 531423, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- trace code [i] based on linear OA(8126, 531449, F81, 9) (dual of [531449, 531423, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(952, 1062898, F9, 9) (dual of [1062898, 1062846, 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, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (44, 53, 265724)-net over F9 | [i] | Net Duplication | |