Special Issue: Interactions Between Ring Theory and Coding Theory

Guest Editors

Prof. Juan Antonio López-Ramos
Department of Mathematics, University of Almeria, Almeria, Spain
Email: jlopez@ual.es


Dr. Daniel Camazon Portela
Department of Mathematics, University of Almeria, Almeria, Spain
Email: danielcp@ual.es

Manuscript Topics


Ring Theory is a mathematical discipline that studies algebraic structures that generalizes fields and where multiplicative commutativity and existence of inverses do not necessarily hold. This branch of Algebra is closely interconnected with many other algebraic branches, providing a mutual feedback that allows them to continue evolving in obtaining new insights and applications. In the case of commutative rings this can be observed through the translation of many geometrical properties of algebraic varieties into properties of associated commutative rings, as well as, in the non-commutative case, the study of non-commutative rings has a deep influence in the development of Non-Commutative Geometry and the study of Quantum Groups. Just to cite a few more examples, we can mention Representation Theory, where elements of a group are represented as invertible matrices or Homology methods that undoubtedly contributed, for instance, to the classification of rings through their representations, also called modules and, the discipline that aims this special issue to study in relation with Ring Theory, which is Coding Theory. Algebraic Coding Theory is the area of Mathematics that searches for encoding/decoding procedures with the main objective of error control. Among the main codes that are studied, we find the so-called AG-codes, an extension of Reed-Solomon codes, not only due to their importance in the birth of the study of families of codes defined from algebraic curves and varieties and being Goppa codes, probably the most widely known family of this type, but also because they have a deep impact in recent applications of Coding Theory for post-quantum Cryptography. But the influence is, at the same time, reciprocal. For instance, some properties of linear codes, that can be thought as ideals in a ring, or modules over a ring, can characterize such a ring as in the case finite Frobenius rings.
Thus, the aim of this special issue is to gather recent advances in both algebraic disciplines, Ring Theory and Coding Theory that interact  and present both results derived from Coding Theory results arising from the study of algebraic codes producing advances in the knowledge of rings and their modules and new contributions to the obtaining of new examples of codes and/or applications induced from the study or application of Ring Theory techniques.


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Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 31 December 2025

Published Papers(1)