  We show that topological mixing, weak mixing and total transitivity are
equivalent for coded systems. We provide an example of a mixing coded system
which cannot be approximated by any increasing sequence of mixing shifts of
finite type, has only periodic points of even period and each set of its
generators consists of blocks of even length. We prove that such an example
cannot be a synchronized system. We also show that a mixing coded systems has
the strong property $P$.
