Multicyclic Codes and Algebraic Dynamical Systems
R. M. Lalasoa
Department of Mathematics and Computer Science, Faculty of Sciences, University of Antananarivo, BOP 906, 101 Antananarivo, Madagascar.
R. Andriamifidisoa *
Higher Polytechnics Institute of Madagascar (ISPM), Ambatomaro, Antsobolo, 101 Antananarivo, Madagascar.
T. J. Rabeherimanana
Department of Mathematics and Computer Science, Faculty of Sciences, University of Antananarivo, BOP 906, 101 Antananarivo, Madagascar.
*Author to whom correspondence should be addressed.
Abstract
We present the structures within group algebras constructed from commutative groups and finite fields. Then we define and construct multicyclic codes in these group algebras. At the end, in the frame of the decoding process, we give a characterization of the locator ideal to the multidimensional case. All of this is done using algebraic dynamical systems, which explains the underlying mathematical objects.
Keywords: Galois group, group algebra, categories and functors, algebraic dynamical system, multicyclic code.