# American Institute of Mathematical Sciences

February  2016, 10(1): 29-43. doi: 10.3934/amc.2016.10.29

## Convolutional codes with a matrix-algebra word-ambient

 1 Department of Algebra and CITIC-UGR, University of Granada, E18071 Granada 2 Department of Computer Sciences and AI, and CITIC, Universidad de Granada, E51001 Ceuta, Spain

Received  November 2014 Revised  July 2015 Published  March 2016

Let $\mathcal{M}_n(\mathbb{F})$be the algebra of $n \times n$ matrices over the finite field $\mathbb{F}$. In this paper we prove that the dual code of each ideal convolutional code in the skew-polynomial ring $\mathcal{M}_n(\mathbb{F})[z;\sigma_U]$ which is a direct summand as a left ideal, is also an ideal convolutional code over $\mathcal{M}_n(\mathbb{F})[z;\sigma_UT]$ and a direct summand as a left ideal. Moreover we provide an algorithm to decide if $\sigma_U$ is a separable automorphism and returns the corresponding separability element, when pertinent.
Citation: José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Convolutional codes with a matrix-algebra word-ambient. Advances in Mathematics of Communications, 2016, 10 (1) : 29-43. doi: 10.3934/amc.2016.10.29
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