Information on Result #1184018
Digital (192, 206, 2097189)-net over F3, using net defined by OOA based on linear OOA(3206, 2097189, F3, 20, 14) (dual of [(2097189, 20), 41943574, 15]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3206, 4194379, F3, 4, 14) (dual of [(4194379, 4), 16777310, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3206, 4194380, F3, 4, 14) (dual of [(4194380, 4), 16777314, 15]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(39, 80, F3, 4, 4) (dual of [(80, 4), 311, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(39, 80, F3, 3, 4) (dual of [(80, 3), 231, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 9, 80)-net over F3, using
- appending kth column [i] based on linear OOA(39, 80, F3, 3, 4) (dual of [(80, 3), 231, 5]-NRT-code), using
- linear OOA(361, 2097150, F3, 4, 7) (dual of [(2097150, 4), 8388539, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(361, 2796200, F3, 4, 7) (dual of [(2796200, 4), 11184739, 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, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
- linear OOA(3136, 2097150, F3, 4, 14) (dual of [(2097150, 4), 8388464, 15]-NRT-code), using
- OOA 4-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 4-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-code), using
- linear OOA(39, 80, F3, 4, 4) (dual of [(80, 4), 311, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3206, 4194380, F3, 4, 14) (dual of [(4194380, 4), 16777314, 15]-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.