Information on Result #1210291
Digital (127, 141, 1198450)-net over F4, using (u, u+v)-construction based on
- digital (13, 20, 79)-net over F4, using
- net defined by OOA [i] based on linear OOA(420, 79, F4, 9, 7) (dual of [(79, 9), 691, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(420, 80, F4, 3, 7) (dual of [(80, 3), 220, 8]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(41, 20, F4, 3, 1) (dual of [(20, 3), 59, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(41, s, F4, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(41, s, F4, 3, 1) for arbitrarily large s, using
- linear OOA(43, 20, F4, 3, 2) (dual of [(20, 3), 57, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(43, 21, F4, 3, 2) (dual of [(21, 3), 60, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(43, 21, F4, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
- appending kth column [i] based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- appending kth column [i] based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(43, 21, F4, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(43, 21, F4, 3, 2) (dual of [(21, 3), 60, 3]-NRT-code), using
- linear OOA(45, 20, F4, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(45, 40, F4, 3, 3) (dual of [(40, 3), 115, 4]-NRT-code), using
- linear OOA(411, 20, F4, 3, 7) (dual of [(20, 3), 49, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 11, 20)-net over F4, using
- linear OOA(41, 20, F4, 3, 1) (dual of [(20, 3), 59, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(420, 80, F4, 3, 7) (dual of [(80, 3), 220, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(420, 79, F4, 9, 7) (dual of [(79, 9), 691, 8]-NRT-code), using
- digital (107, 121, 1198371)-net over F4, using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 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.