ON THE ALGEBRAIC PARAMETERS OF CONVOLUTIONAL CODES WITH CYCLIC STRUCTURE-Reference-Cited by-同舟云学术

ON THE ALGEBRAIC PARAMETERS OF CONVOLUTIONAL CODES WITH CYCLIC STRUCTURE

Published:2006-02 Issue:01 Volume:05 Page:53-76
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

GLUESING-LUERSSEN HEIDE¹,LANGFELD BARBARA²

Affiliation:

1. University of Groningen, Department of Mathematics, P.O. Box 800, 9700 AV Groningen, The Netherlands

2. Kombinatorische Geometrie (M9), Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany

Abstract

In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [4] that only certain combinations of the algebraic parameters (field size, length, dimension, and Forney indices) can occur for such cyclic codes. We will investigate whether all these combinations can indeed be realized by a suitable cyclic code and, if so, how to construct such a code. A complete characterization and construction will be given for minimal cyclic codes. It is derived from a detailed investigation of the units in the skew-polynomial ring.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498806001570

Reference18 articles.

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2. Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems

3. On Cyclic Convolutional Codes

4. Fundamentals of Error-Correcting Codes

5. Fundamentals of Convolutional Coding

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