On behaviors and convolutional codes

On behaviors and convolutional codes

It is well known that a convolutional code is essentially a linear system def ined over a finite field. In this paper we elaborate on this connect ion. W e will def ine a convolutional code as the dual of a complete linear behavior in the sense of W illems. Using ideas from systems theory, we descr ibe a set of general ized first-order descriptions for convolutional codes. As an application of ...

On Behaviors and Convolutional

| It is well known that a convolutional code is essentially a linear system deened over a nite eld. In this paper we elaborate on this connection. We will deene convolutional codes as the dual of a complete linear behavior in the sense of Willems. Using ideas from systems theory we describe a set of generalized rst order descriptions for convolutional codes. As an application of these ideas, we...

On Woven Convolutional Codes

On cyclic convolutional codes

We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [15, 18]. Codes of this type are described as submodules of F[z]n with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result of [15], we show in a purely algebraic setting that these ideals are always principal. This leads t...

New convolutional codes from old convolutional codes

In this paper, starting with a family of convolutional codes, we construct a new convolutional code and we introduce also necessary and sufficient conditions in order that the new convolutional code is MDS.