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Axioms
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Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd...
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Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 April 2025) | Viewed by 990

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 will study new encoding and decoding procedures based on different algebraic structures by applying the latter 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 processes. These algebraic structures include commutative, computational, ordered, and hypercompositional algebras, emphasizing new combinatorial aspects related to lattice, category, and graph theories and modelling.

This Special Issue welcomes original, high-level contributions presenting a connection between algebraic structures and coding theory or cryptography. New theoretical aspects and practical applications representing current research directions are also appreciated, alongside high-quality review papers.

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

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

Related Special Issue

Published Papers (3 papers)

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Research

22 pages, 307 KiB  
Article
An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications
by Tahsin Oner, Rajesh Neelamegarajan, Ravi Kumar Bandaru and Hashem Bordbar
Axioms 2025, 14(5), 338; https://doi.org/10.3390/axioms14050338 - 28 Apr 2025
Viewed by 61
Abstract
This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations [...] Read more.
This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations of bipolar fuzzy filters via level sets and conditions under which they become implicative filters. These findings enhance the theoretical framework of many-valued logic and offer practical applications in decision-making, image processing, and spatial reasoning under uncertainty. Our work provides a foundation for advanced fuzzy systems handling complex, contradictory information. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)
16 pages, 299 KiB  
Article
On the Equational Theory of Lattice-Based Algebras for Layered Graphs
by Zhe Yu, Hao Zhan, Yiheng Wang, Zhe Lin and Fei Liang
Axioms 2025, 14(4), 257; https://doi.org/10.3390/axioms14040257 - 28 Mar 2025
Viewed by 150
Abstract
Layered algebras are introduced and used to express layered graphs. Layered graphs are considered to be a highly effective abstract tool to manage the difficulty in conceptualizing and reasoning regarding complex systems related to coding in email exchange and access control in security. [...] Read more.
Layered algebras are introduced and used to express layered graphs. Layered graphs are considered to be a highly effective abstract tool to manage the difficulty in conceptualizing and reasoning regarding complex systems related to coding in email exchange and access control in security. In the present paper, we study the varieties of several classes of lattice-based layer algebras and show that all these varieties have decidable equational theory via a finite model property. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)
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28 pages, 358 KiB  
Article
Idempotent Triangular Matrices over Additively Idempotent Semirings: Decompositions into Products of Semicentral Idempotents
by Dimitrinka Vladeva
Axioms 2025, 14(2), 137; https://doi.org/10.3390/axioms14020137 - 15 Feb 2025
Viewed by 342
Abstract
The explicit forms of idempotent and semicentral idempotent triangular matrices over an additively idempotent semiring are obtained. We define a diamond composition of idempotents and give a representation of an idempotent n×n matrix as an (n−1)th [...] Read more.
The explicit forms of idempotent and semicentral idempotent triangular matrices over an additively idempotent semiring are obtained. We define a diamond composition of idempotents and give a representation of an idempotent n×n matrix as an (n−1)th degree of a sum of diamond compositions of semicentral idempotents. We construct a decomposition of a strictly upper matrix, a unitriangular matrix, and a nil-clean matrix by semicentral idempotents. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)
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