On behaviors and convolutional codes

Authors:
J. Rosenthal;J. M. Schumacher;E. V. York
Affiliations:
Dept. of Math., Notre Dame Univ., IN;-;-
Venue:
IEEE Transactions on Information Theory - Part 1
Year:
2006

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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 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