Meaning of the $m$ power of a modular world
The notation $(Z_{26})^m$ means the $m$-fold cartesian product of $Z_{26}$.  This is a set whose elements are all tuples of length $m$ with components in $Z_{26}$.  For example, $(Z_2)^2$ means the set of tuples (0,0), (0,1), (1,0), (1,1), where $Z_2$ alone is taken to mean the set of integers modulo 2, i.e. 0 or 1.  In this context, you can read $(Z_{26})^m$ as the set of strings that are $m$ English letters long.

(Beware: Sometimes $Z$ means the center of a group, not the integers, so I prefer to write the unambiguous $\mathbb Z$.  Sometimes $Z_p$ or $\mathbb Z_p$ means the $p$-adic integers, so I prefer to write $\mathbb Z/p\mathbb Z$ which is the unambiguous quotient of $\mathbb Z$ by the ideal $p\mathbb Z$, i.e. the integers modulo $p$.  But in this case context suggests that $Z_{26}$ means the set of integers modulo 26, corresponding to the English alphabet.)