It is well known that a convolutional code can be viewed as a linear system over a finite field. In this paper we develop this viewpoint for convolutional codes using several recent innovations from the systems theory literature. In particular we define codes as behaviors of a set of compact support time trajectories over a vector space. We also consider several different representations of codes, in particular generalized first order representations. As an application of these ideas, we present a BCH construction technique for convolutional codes that yields optimal high rate codes.

Convolutional codes (msc 94B10), Minimal systems representations (msc 93B20)
CWI
Department of Operations Research, Statistics, and System Theory [BS]

Rosenthal, J, Schumacher, J.M, & York, E.V. (1995). The behavior of convolution codes. Department of Operations Research, Statistics, and System Theory [BS]. CWI.