RAPPORT The behavior of convolutional codes

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