This paper discusses the issue of the Persistent Excitation (PE) conditions in the context of identification for dynamical systems defined over a finite field. The work is motivated by the fact that the asymptotical property of the PE conditions for dynamical systems defined over the field of real numbers is no longer valid in the case of systems defined over finite fields. The special class of switched linear discrete-time systems for which the mode is assumed to be unknown is considered. A necessary and sufficient condition that provides the minimum amount of data required for the identification is first proposed. Next, a necessary condition is derived that gives the structural condition the system must satisfy, regardless of the availability of data. Finally, some computational aspects are discussed and examples are given to illustrate the validity of the proposed results. (C) 2014 Elsevier Ltd. All rights reserved.