Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.6
Journals
Axioms
Special Issues
Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 3rd...
share announcement

Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 3rd Edition

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

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1562

Special Issue Editor

Dr. Hashem Bordbar

E-Mail Website
Guest 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 study new encoding and decoding procedures based on different algebraic structures. In other words, 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 hypercompositional algebras, emphasizing new combinatorial aspects related to lattice theory, category theory, 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 250 words) can be sent to the Editorial Office for assessment.

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

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Related Special Issues

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

14 pages, 303 KB  
Article
A Novel Cryptanalysis of the Cubic Pell RSA Variant
by Brahim Chnioune, Mohammed Rahmani, Abderrahmane Nitaj and Mhammed Ziane
Axioms 2026, 15(5), 347; https://doi.org/10.3390/axioms15050347 - 8 May 2026
Viewed by 180
Abstract
A new RSA variant based on the cubic Pell curve operates with a modulus N=pq where the encryption and the decryption exponents e and d are linked by the congruence [...] Read more.
A new RSA variant based on the cubic Pell curve operates with a modulus N=pq where the encryption and the decryption exponents e and d are linked by the congruence ed≡1 (mod(p−1)2(q−1)2). At Africacrypt 2025, Rahmani and Nitaj demonstrated that this scheme is susceptible to lattice-based attacks when the secret exponent d is small. In this work, we present a refined attack on the same scheme when the prime factors p and q share a sufficient portion of their least significant bits (LSBs). Our new method extends the former results, and yields improved bounds on the decryption exponents. Leveraging a combination of Coppersmith-type techniques and lattice methods, our approach is capable of recovering the RSA prime factors in polynomial time. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 3rd Edition)
►▼ Show Figures

Figure 1

21 pages, 307 KB  
Article
Unifying Bipolar and Cubic Set Theories: Ideals in Sheffer Stroke Hilbert Algebras
by Amal S. Alali, Hashem Bordbar, Ravikumar Bandaru, Rajesh Neelamegarajan and Tahsin Oner
Axioms 2026, 15(5), 301; https://doi.org/10.3390/axioms15050301 - 22 Apr 2026
Viewed by 239
Abstract
In recent years, the study of generalized fuzzy structures in algebraic systems has attracted considerable attention due to their ability to represent uncertainty and bipolar information. In this paper, we introduce the notion of cubic bipolar ideals in the framework of Sheffer stroke [...] Read more.
In recent years, the study of generalized fuzzy structures in algebraic systems has attracted considerable attention due to their ability to represent uncertainty and bipolar information. In this paper, we introduce the notion of cubic bipolar ideals in the framework of Sheffer stroke Hilbert algebras. This concept integrates the descriptive capability of cubic sets with the dual representation of bipolar information, providing a broader perspective for investigating algebraic structures associated with the Sheffer stroke operation. We establish the definition of cubic bipolar ideals and investigate several of their fundamental properties. In particular, the structural behavior of these ideals is examined within Sheffer stroke Hilbert algebras. Furthermore, the preservation of cubic bipolar ideals under algebraic homomorphisms is analyzed through the study of images and preimages. The Cartesian product of cubic bipolar ideals is also discussed, and conditions ensuring the stability of the resulting structures are obtained. The results presented here contribute to the development of fuzzy algebraic theory and extend existing approaches to Sheffer stroke-based algebraic systems. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 3rd Edition)
23 pages, 434 KB  
Article
Multiary Gradings
by Steven Duplij
Axioms 2026, 15(3), 197; https://doi.org/10.3390/axioms15030197 - 6 Mar 2026
Viewed by 453
Abstract
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading [...] Read more.
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading group operations. Key results include quantization rules connecting arities, classification of graded homomorphisms, the First Isomorphism Theorem for graded polyadic algebras and concrete examples including ternary superalgebras and polynomial algebras over n-ary matrices. The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 3rd Edition)
16 pages, 318 KB  
Article
Odd Right-End Numerical Semigroups
by María Ángeles Moreno-Frías and José Carlos Rosales
Axioms 2026, 15(3), 189; https://doi.org/10.3390/axioms15030189 - 5 Mar 2026
Viewed by 311
Abstract
An odd right-end semigroup (hereinafter Ore semigroup) is a numerical semigroup S verifying that x+1∈S for every x∈S∖{0} such that x is even. The introduction and study of these semigroups is the purpose [...] Read more.
An odd right-end semigroup (hereinafter Ore semigroup) is a numerical semigroup S verifying that x+1∈S for every x∈S∖{0} such that x is even. The introduction and study of these semigroups is the purpose of the present work. In particular, we will give some algorithms which compute all Ore semigroups with a given genus, a fixed Frobenius number and a specific multiplicity. We will see that if X is a set of positive integers, then there exists the smallest Ore semigroup, under the inclusion sets, that contains X. We will denote this semigroup by θ[X] and present an algorithm to calculate it. Finally, we will study the embedding dimension, the Frobenius number, and the genus of Ore semigroups of the form θ[{m}], where m is a positive integer. As a consequence of this study, we will prove that this kind of semigroup satisfies Wilf’s conjecture. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 3rd Edition)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop