State representations of convolutional codes over a finite ring

Abstract

In this paper we study finite support convolutional codes over Z_{p^r} by means of an input-state-output representation. We show that the set of finite weight input-state-output trajectories associated to this type of representations has the structure of a Z_{p^r}-submodule of Z_{p^r}^n and therefore is a (finite support) convolutional code. Fundamental system-theoretical properties such as observability, reachability or minimality, are investigated in this context.