Mathematical definition of homophonic substitution ciphers

• To each $a\in \mathcal{A}$ associate a set $H(a)$ of strings of $t$ symbols, where $H(a)$, $a\in \mathcal{A}$ are pairwise disjoint.
• Replace each $a$ with a randomly chosen string from $H(a)$. To decrypt a string $c$ of $t$ symbols, one must determine an $a\in \mathcal{A}$ such that $c\in H(a)$.
• The key for the cipher is the sets $H(a)$.