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Axioms
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Computational Algebra, Coding Theory and Cryptography: Theory and Applications
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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 October 2024 | Viewed by 4272

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 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 (4 papers)

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Research

10 pages, 267 KiB  
Article
A Class of Bounded Iterative Sequences of Integers
by Artūras Dubickas
Axioms 2024, 13(2), 107; https://doi.org/10.3390/axioms13020107 - 04 Feb 2024
Viewed by 1020
Abstract
In this note, we show that, for any real number τ∈[12,1), any finite set of positive integers K and any integer s1≥2, the sequence of integers [...] Read more.
In this note, we show that, for any real number τ∈[12,1), any finite set of positive integers K and any integer s1≥2, the sequence of integers s1,s2,s3,… satisfying si+1−si∈K if si is a prime number, and 2≤si+1≤τsi if si is a composite number, is bounded from above. The bound is given in terms of an explicit constant depending on τ,s1 and the maximal element of K only. In particular, if K is a singleton set and for each composite si the integer si+1 in the interval [2,τsi] is chosen by some prescribed rule, e.g., si+1 is the largest prime divisor of si, then the sequence s1,s2,s3,… is periodic. In general, we show that the sequences satisfying the above conditions are all periodic if and only if either K={1} and τ∈[12,34) or K={2} and τ∈[12,59). Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications)
13 pages, 308 KiB  
Article
Sheffer Stroke Hilbert Algebras Stabilizing by Ideals
by Tugce Katican and Hashem Bordbar
Axioms 2024, 13(2), 97; https://doi.org/10.3390/axioms13020097 - 30 Jan 2024
Viewed by 751
Abstract
This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these [...] Read more.
This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these subsets by investigating whether these sets are ideals or not. Furthermore, we investigate whether the introduced subsets of Sheffer stroke Hilbert algebras are minimal ideals. Afterwards, we define stabilizers in a Sheffer stroke Hilbert algebra and obtain their set theoretical properties. As an implementation of the theoretical findings, we present numerous examples and illustrative remarks to guide readers. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications)
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15 pages, 366 KiB  
Article
Remarks on Conjectures in Block Theory of Finite Groups
by Manal H. Algreagri and Ahmad M. Alghamdi
Axioms 2023, 12(12), 1103; https://doi.org/10.3390/axioms12121103 - 06 Dec 2023
Viewed by 823
Abstract
In this paper, we focus on Brauer’s height zero conjecture, Robinson’s conjecture, and Olsson’s conjecture regarding the direct product of finite groups and give relative versions of these conjectures by restricting them to the algebraic concept of the anchor group of an irreducible [...] Read more.
In this paper, we focus on Brauer’s height zero conjecture, Robinson’s conjecture, and Olsson’s conjecture regarding the direct product of finite groups and give relative versions of these conjectures by restricting them to the algebraic concept of the anchor group of an irreducible character. Consider G to be a finite simple group. We prove that the anchor group of the irreducible character of G with degree p is the trivial group, where p is an odd prime. Additionally, we introduce the relative version of the Green correspondence theorem with respect to this group. We then apply the relative versions of these conjectures to suitable examples of simple groups. Classical and standard theories on the direct product of finite groups, block theory, and character theory are used to achieve these results. Full article
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications)
18 pages, 408 KiB  
Article
Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields
by Jorge Jimenez, María Luisa Serrano, Branimir Šešelja and Andreja Tepavčević
Axioms 2023, 12(8), 757; https://doi.org/10.3390/axioms12080757 - 01 Aug 2023
Viewed by 707
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
(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications)
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