Information on Result #1193724
Digital (96, 109, 2796241)-net over F9, using net defined by OOA based on linear OOA(9109, 2796241, F9, 15, 13) (dual of [(2796241, 15), 41943506, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9109, 5592483, F9, 3, 13) (dual of [(5592483, 3), 16777340, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9109, 5592484, F9, 3, 13) (dual of [(5592484, 3), 16777343, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(911, 82, F9, 3, 6) (dual of [(82, 3), 235, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 11, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(5,81) in PG(10,9)) for nets [i] based on digital (0, 6, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base reduction for projective spaces (embedding PG(5,81) in PG(10,9)) for nets [i] based on digital (0, 6, 82)-net over F81, using
- extracting embedded OOA [i] based on digital (5, 11, 82)-net over F9, using
- linear OOA(998, 5592402, F9, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- linear OOA(911, 82, F9, 3, 6) (dual of [(82, 3), 235, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(9109, 5592484, F9, 3, 13) (dual of [(5592484, 3), 16777343, 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, 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 (205, 218, 5592482)-net over F3 | [i] | Trace Code for Nets | |