  As a generalization of cyclic codes of length p^s over F_{p^a}, we study
n-dimensional cyclic codes of length p^{s_1} X ... X p^{s_n} over F_{p^a}
generated by a single "monomial". Namely, we study multi-variable cyclic codes
of the form <(x_1 - 1)^{i_1} ... (x_n - 1)^{i_n}> in F_{p^a}[x_1...x_n] / <
x_1^{p^{s_1}}-1, ..., x_n^{p^{s_n}}-1 >. We call such codes monomial-like
codes. We show that these codes arise from the product of certain single
variable codes and we determine their minimum Hamming distance. We determine
the dual of monomial-like codes yielding a parity check matrix. We also present
an alternative way of constructing a parity check matrix using the Hasse
derivative. We study the weight hierarchy of certain monomial like codes. We
simplify an expression that gives us the weight hierarchy of these codes.
