  The concept of "$A$-coupled-expanding" map for a transition matrix $A$ has
been studied as one of the most important criteria of chaos in the past years.
In this paper, the lower bound of the topological entropy for strictly
$A$-coupled-expanding maps is studied as a criterion for chaos in the sense of
Li-Yorke, which is less conservative and more generalized than the latest
result is presented. Furthermore, some conditions for $A$-coupled-expanding
maps excluding the strictness to be factors of subshifts of finite type are
derived. In addition, the topological entropy of
partition-$A$-coupled-expanding map, which is put forward in this paper, is
further estimated on compact metric spaces. Particularly, the topological
entropy for partition-$A$-coupled-expanding circle maps is given, with that for
the Kasner map being calculated for illustration and verification.
