Communications of the
Korean Mathematical Society CKMS

Let $R_e=\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$, where $p$ is a prime number, $ e $ is a positive integer and $u^e=0$. In this paper, we first characterize the structure of cyclic codes of length $p^s$ over $R_e$. These codes will be classified into $2^e $ distinct types. Among other results, in the case that $e=4$, the torsion codes of cyclic codes of length $ p^s $ over $ R_4$ are obtained. Also, we present some examples of cyclic codes of length $p^s $ over $R_e$.

Keywords: Chain ring, cyclic code, torsion code

MSC numbers: 94B15, 16S36