Contraction of Cyclic Codes Over Finite Chain Rings

Abstract

Let $\text{R}$ be a commutative finite chain ring of invariants $(q,s)$ and $\Gamma (\text{R})$ the Teichmüller's set of $\text{R}.$ In this paper, the trace representation cyclic $\text{R}$-linear codes of length $\ell ,$ is presented, when $\text{gcd}(\ell ,q)=1.$ We will show that the contractions of some cyclic $\text{R}$-linear codes of length $u\ell$ are $\gamma$-constacyclic $\text{R}$-linear codes of length $\ell ,$ where $\gamma \in \Gamma (\text{R})$ and the multiplicative order of is $u.$