Contraction of cyclic codes over finite chain rings

In this paper, $R$ is a finite chain ring with residue field ${\mathbb{F}}_q$ and $\gamma$ is a unit in $R.$ By assuming that the multiplicative order $u$ of $\gamma$ is coprime to $q,$ we give the trace-representation of any simple-root $\gamma$-constacyclic code over $R$ of length $?,$ and on the other hand show that any cyclic code over $R$ of length $u?$ is a direct sum of trace-representable cyclic codes. Finally, we characterize the simple-root, contractable and cyclic codes over $R$ of length $u?$ into $\gamma$-constacyclic codes of length $?.$