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On behaviors and convolutional codes


Rosenthal, J; Schumacher, J; York, E (1996). On behaviors and convolutional codes. IEEE Transactions on Information Theory, 42(6, par):1881-1891.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:algebraic construction, convolutional codes, finite field, generalized first-order descriptions, linear behavior, linear codes, linear system, matrix representations, module theory, systems theory
Language:English
Date:1996
Deposited On:17 Mar 2010 13:19
Last Modified:05 Apr 2016 13:27
Publisher:IEEE
ISSN:0018-9448
Publisher DOI:https://doi.org/10.1109/18.556682

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