Information on Result #1022030
Linear OOA(9137, 5592912, F9, 3, 15) (dual of [(5592912, 3), 16778599, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(923, 510, F9, 3, 7) (dual of [(510, 3), 1507, 8]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(91, 91, F9, 3, 1) (dual of [(91, 3), 272, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 3, 1) for arbitrarily large s, using
- linear OOA(93, 91, F9, 3, 2) (dual of [(91, 3), 270, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- Hamming code H(3,9) [i]
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- linear OOA(95, 164, F9, 3, 3) (dual of [(164, 3), 487, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(95, 211, F9, 3, 3) (dual of [(211, 3), 628, 4]-NRT-code), using
- linear OOA(914, 164, F9, 3, 7) (dual of [(164, 3), 478, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 7, 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
- trace code for nets [i] based on digital (0, 7, 82)-net over F81, using
- extracting embedded OOA [i] based on digital (7, 14, 164)-net over F9, using
- linear OOA(91, 91, F9, 3, 1) (dual of [(91, 3), 272, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(9114, 5592402, F9, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
- trace code [i] based on linear OOA(8157, 2796201, F81, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- trace code [i] based on linear OOA(8157, 2796201, F81, 3, 15) (dual of [(2796201, 3), 8388546, 16]-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.
Other Results with Identical Parameters
None.
Depending Results
None.