Information on Result #1119358
Linear OOA(3231, 5033652, F3, 5, 13) (dual of [(5033652, 5), 25168029, 14]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(328, 1677884, F3, 5, 4) (dual of [(1677884, 5), 8389392, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(328, 2391484, F3, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(328, 2391485, F3, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F3, using
- OOA stacking with additional row [i] based on linear OOA(328, 2391485, F3, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(328, 2391484, F3, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
- linear OOA(360, 1677884, F3, 5, 6) (dual of [(1677884, 5), 8389360, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(360, 2796201, F3, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- discarding factors / shortening the dual code based on linear OOA(360, 2796201, F3, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
- linear OOA(3143, 1677884, F3, 5, 13) (dual of [(1677884, 5), 8389277, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(322, 164, F3, 5, 6) (dual of [(164, 5), 798, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 22, 164)-net over F3, using
- trace code for nets [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
- trace code for nets [i] based on digital (5, 11, 82)-net over F9, using
- extracting embedded OOA [i] based on digital (16, 22, 164)-net over F3, using
- linear OOA(3121, 1677720, F3, 5, 13) (dual of [(1677720, 5), 8388479, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3121, 8388600, F3, 13) (dual of [8388600, 8388479, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- OOA 5-folding [i] based on linear OA(3121, 8388600, F3, 13) (dual of [8388600, 8388479, 14]-code), using
- linear OOA(322, 164, F3, 5, 6) (dual of [(164, 5), 798, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
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
None.