Information on Result #2798183
Linear OOA(3185, 2097182, F3, 4, 17) (dual of [(2097182, 4), 8388543, 18]-NRT-code), using 31 times duplication based on linear OOA(3184, 2097182, F3, 4, 17) (dual of [(2097182, 4), 8388544, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(318, 32, F3, 4, 8) (dual of [(32, 4), 110, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 18, 32)-net over F3, using
- trace code for nets [i] based on digital (1, 9, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- trace code for nets [i] based on digital (1, 9, 16)-net over F9, using
- extracting embedded OOA [i] based on digital (10, 18, 32)-net over F3, using
- linear OOA(3166, 2097150, F3, 4, 17) (dual of [(2097150, 4), 8388434, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3166, 8388600, F3, 17) (dual of [8388600, 8388434, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 4-folding [i] based on linear OA(3166, 8388600, F3, 17) (dual of [8388600, 8388434, 18]-code), using
- linear OOA(318, 32, F3, 4, 8) (dual of [(32, 4), 110, 9]-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.