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 $q\equiv 1(mod~ m_{ j}), j\geq 2$, where $q=p^{ r}$ is the cardinality of residue field of $\mathfrak{ R}$.
Categories: cs.IT math.IT