Covert channels are a security threat for information systems, since they permit illegal flows, and sometimes leaks, of classified data. Although numerous descriptions have been given at a concrete level, relatively little work has been carried out at a more abstract level, outside probabilistic models. In this paper, we propose a definition of covert channels based on encoding and decoding binary messages with transducers, in a finite transition system. We first compare this notion of covert channel with a similar one called iterated interference. We then give a necessary condition for the existence of a covert channel. Unfortunately, in the general case of our setting, it turns out that the existence of a covert channel is undecidable. However, restricting to functional systems, we obtain a PTIME procedure to decide the existence of a covert channel.