Let $\Sigma$ be a given alphabet. Is there a way to code up Deterministic Finite state Automata (DFA) over $\Sigma$ as strings of $\Sigma$ in such a way that the corresponding subset of $\Sigma^*$ is a regular language?
For example for Turing machines, the set of codes of Turing machines over a fixed alphabet is decidable, and we can speak of decidable sets of Turing machines (through their codes).
Of course we can also speak of regular sets of DFA's (through their codes). Is the set of all DFA's regular in this sense?