On Behaviors and Convolutionail Codes

It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We define a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979). Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these ideas, we present a new algebraic construction for convolutional codes. IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 42, NO. 6, NOVEMBER 1996 1881 On Behaviors and Convolutionail Codes Joachim Rosenthal, Senior Member, IEEE, J. M. Schumacher, Member, IEEE, and Eric V. York, Student Member, IEEE Abstract-It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We will define a convolutional code as the dual of a complete linear behavior in the sense of Willems. Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these ideas, we present a new algebraic construction for convolutional codes.It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We will define a convolutional code as the dual of a complete linear behavior in the sense of Willems. Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these ideas, we present a new algebraic construction for convolutional codes. Zndex TermsConvolutional codes, behaviors, duality, firstorder representations, code constructions.