On a class of repeated-root monomial-like abelian codes

In this paper we study polycyclic codes of length $p^{s_1} \times \cdots \times p^{s_n}$\ over $\F_{p^a}$\ generated by a single monomial. These codes form a special class of abelian codes. We show that these codes arise from the product of certain single variable codes and we determine their minimum Hamming distance. Finally we extend the results of Massey et. al. in \cite{MASSEY_1973} on the weight retaining property of monomials in one variable to the weight retaining property of monomials in several variables.