Information on Result #2874056
Linear OOA(3247, 5033412, F3, 5, 14) (dual of [(5033412, 5), 25166813, 15]-NRT-code), using 31 times duplication based on linear OOA(3246, 5033412, F3, 5, 14) (dual of [(5033412, 5), 25166814, 15]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(328, 1677804, F3, 5, 4) (dual of [(1677804, 5), 8388992, 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(361, 1677804, F3, 5, 7) (dual of [(1677804, 5), 8388959, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(361, 2796200, F3, 5, 7) (dual of [(2796200, 5), 13980939, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(361, 8388601, F3, 7) (dual of [8388601, 8388540, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(361, 8388601, F3, 7) (dual of [8388601, 8388540, 8]-code), using
- discarding factors / shortening the dual code based on linear OOA(361, 2796200, F3, 5, 7) (dual of [(2796200, 5), 13980939, 8]-NRT-code), using
- linear OOA(3157, 1677804, F3, 5, 14) (dual of [(1677804, 5), 8388863, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(321, 84, F3, 5, 7) (dual of [(84, 5), 399, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 21, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 7, 28)-net over F27, using
- extracting embedded OOA [i] based on digital (14, 21, 84)-net over F3, using
- linear OOA(3136, 1677720, F3, 5, 14) (dual of [(1677720, 5), 8388464, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OOA 5-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-code), using
- linear OOA(321, 84, F3, 5, 7) (dual of [(84, 5), 399, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(328, 1677804, F3, 5, 4) (dual of [(1677804, 5), 8388992, 5]-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.