On behaviors and convolutional codes

It is well known that a convolutional code is essentially a linear system def ined over a finite field. In this paper we elaborate on this connect ion. W e will def ine a convolutional code as the dual of a complete linear behavior in the sense of W illems. Using ideas from systems theory, we descr ibe a set of general ized first-order descriptions for convolutional codes. As an application of these ideas, we present a new algebraic construction for convolutional codes.