Special Issue "Computational Algebra, Coding Theory and Cryptography: Theory and Applications"

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: 20 February 2024 | Viewed by 989

Special Issue Editor

Center for Information Technologies and Applied Mathematics, University of Nova Gorica, SI-5000 Nova Gorica, Slovenia
Interests: algebraic coding theory; commutative algebra; hypercompositional algebra; ordered algebra; lattice theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue’s main purpose is to explore new encoding and decoding procedures based on different algebraic structures. In other words, this refers to the application of algebraic structures in error-control codes to find new algorithms that increase the number of errors that can be corrected and the speed of the encoding and decoding procedure. These algebraic structures have included commutative algebras, computational algebras, ordered algebras and hyper compositional algebras, emphasizing new combinatorial aspects related to lattice theory, theory of category, graph theory, and modeling.

This Special Issue accepts original and high-level contributions, where a connection between algebraic structures and coding theory or cryptography is presented. New theoretical aspects as well as practical applications representing current research directions on this topic are welcome. We also invite authors to submit high-quality review papers on the aforementioned topic.

Dr. Hashem Bordbar
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • algebraic structures
  • coding theory
  • cryptography
  • linear codes
  • quantum codes
  • polycyclic codes
  • self-dual codes
  • Hermitian codes
  • quasicyclic codes
  • codes over rings

Published Papers (1 paper)

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Research

18 pages, 408 KiB  
Article
Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields
Axioms 2023, 12(8), 757; https://doi.org/10.3390/axioms12080757 - 01 Aug 2023
Viewed by 446
Abstract
Omega rings (Ω-rings) (and other related structures) are lattice-valued structures (with Ω being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, Ω-ideals are introduced, and natural connections [...] Read more.
Omega rings (Ω-rings) (and other related structures) are lattice-valued structures (with Ω being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, Ω-ideals are introduced, and natural connections with Ω-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over Ω-fields is developed. Full article
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