# Clarification on matrix notation subscript and superscript notation

If a matrix C exists in integers $\mathcal{Z}_q^{mxl}$ what does this mean?

I think you mean $\mathbb{Z}_p^{m\times l}$. If so, this is probably being used to denote the set of $m\times l$ matrices over $\mathbb{Z}_p$, which is used to denote either the group of integers modulo $p$, or the $p$-adic integers. You should be able to determine this from the context.