Information on Result #1190448
Digital (96, 109, 1921625)-net over F7, using net defined by OOA based on linear OOA(7109, 1921625, F7, 15, 13) (dual of [(1921625, 15), 28824266, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(7109, 3843251, F7, 3, 13) (dual of [(3843251, 3), 11529644, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7109, 3843252, F7, 3, 13) (dual of [(3843252, 3), 11529647, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(711, 50, F7, 3, 6) (dual of [(50, 3), 139, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 11, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) for nets [i] based on digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) for nets [i] based on digital (0, 6, 50)-net over F49, using
- extracting embedded OOA [i] based on digital (5, 11, 50)-net over F7, using
- linear OOA(798, 3843202, F7, 3, 13) (dual of [(3843202, 3), 11529508, 14]-NRT-code), using
- trace code [i] based on linear OOA(4949, 1921601, F49, 3, 13) (dual of [(1921601, 3), 5764754, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4949, 5764803, F49, 13) (dual of [5764803, 5764754, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4949, 5764805, F49, 13) (dual of [5764805, 5764756, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(4949, 5764801, F49, 13) (dual of [5764801, 5764752, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(4949, 5764805, F49, 13) (dual of [5764805, 5764756, 14]-code), using
- OOA 3-folding [i] based on linear OA(4949, 5764803, F49, 13) (dual of [5764803, 5764754, 14]-code), using
- trace code [i] based on linear OOA(4949, 1921601, F49, 3, 13) (dual of [(1921601, 3), 5764754, 14]-NRT-code), using
- linear OOA(711, 50, F7, 3, 6) (dual of [(50, 3), 139, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(7109, 3843252, F7, 3, 13) (dual of [(3843252, 3), 11529647, 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
None.