An Algorithm to find the Generators of Multidimensional Cyclic Codes over a Finite Chain Ring

The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring $\mathfrak{R}$. An algorithm to find the generator polynomials of $n$ dimensional ($n$D) cyclic codes of length $m_1{m}_2\dots m_n$ over $\mathfrak{R}$ has been developed using the generator polynomials of cyclic codes over $\mathfrak{R}$. Additionally, the generators of $n$D cyclic codes with length $m_1{m}_2\dots m_n$ over $\mathfrak{R}$ have been obtained as separable polynomials for the case $q\equiv 1(mod{m}_j),j\ge 2$, where $q=p^r$ is the cardinality of residue field of $\mathfrak{R}$.