Mathematics for Algebraic Coding Theory and Cryptography

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "A: Algebra and Logic".

Deadline for manuscript submissions: 30 April 2026 | Viewed by 1057

Special Issue Editor


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Guest Editor
1. Department of Mathematics, Sami Shamoon College of Engineering, Ashdod 77245, Israel
2. Department of Informatics, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1797 Sofia, Bulgaria
Interests: public key cryptography; semiring theory; fuzzy graphs

Special Issue Information

Dear Colleagues,

This Special Issue, "Mathematics for Algebraic Coding Theory and Cryptography", is dedicated to highlighting cutting-edge research in two fundamental areas of modern information security and data integrity: algebraic coding theory and cryptography. These fields are essential for developing secure, efficient, and reliable systems for communication and data protection.

Algebraic coding theory, which provides techniques to detect and correct errors in data transmission, is essential for digital communications, from satellite and cellular systems to storage devices. Cryptography, meanwhile, maintains the confidentiality, integrity, and authenticity of data across various applications, including secure messaging, e-commerce, blockchain technology, artificial intelligence, healthcare, and telecommunication networks.

This issue will feature both theoretical developments and practical applications, showcasing innovations in cryptographic protocols, error-correcting codes, and secure algorithms. By bringing together contributions from leading experts, this collection aims to reflect the latest advancements in these areas, offering a valuable resource for researchers, practitioners, and students interested in the mathematical foundations and future directions of coding theory and cryptography.

Dr. Mariana I. Durcheva
Guest Editor

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Keywords

  • algebraic coding theory
  • error-correcting codes
  • public-key cryptography
  • symmetric-key cryptography
  • post-quantum algebraic cryptography
  • secure communication
  • computational complexity in cryptography

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Published Papers (2 papers)

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Research

22 pages, 290 KiB  
Article
Optimal Linear Codes and Their Hulls
by Stefka Bouyuklieva and Mariya Dzhumalieva-Stoeva
Mathematics 2025, 13(15), 2491; https://doi.org/10.3390/math13152491 - 2 Aug 2025
Viewed by 228
Abstract
The hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension. The focus is on [...] Read more.
The hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension. The focus is on the lengths at which self-orthogonal (respectively, LCD) optimal codes exist at fixed dimension. Full article
(This article belongs to the Special Issue Mathematics for Algebraic Coding Theory and Cryptography)
13 pages, 323 KiB  
Article
Application-Oriented Study of Next-Generation Alternant Codes over Gaussian Integers for Secure and Efficient Communication
by Muhammad Sajjad and Nawaf A. Alqwaifly
Mathematics 2025, 13(14), 2263; https://doi.org/10.3390/math13142263 - 13 Jul 2025
Viewed by 376
Abstract
This paper presents the construction and analysis of a novel class of alternant codes over Gaussian integers, aimed at enhancing error correction capabilities in high-reliability communication systems. These codes are constructed using parity-check matrices derived from finite commutative local rings with unity, specifically [...] Read more.
This paper presents the construction and analysis of a novel class of alternant codes over Gaussian integers, aimed at enhancing error correction capabilities in high-reliability communication systems. These codes are constructed using parity-check matrices derived from finite commutative local rings with unity, specifically Zn[i], where i2=1. A detailed algebraic investigation of the polynomial xn1 over these rings is conducted to facilitate the systematic construction of such codes. The proposed alternant codes extend the principles of classical BCH and Goppa codes to complex integer domains, enabling richer algebraic structures and greater error-correction potential. We evaluate the performance of these codes in terms of error correction capability, and redundancy. Numerical results show that the proposed codes outperform classical short-length codes in scenarios requiring moderate block lengths, such as those applicable in certain segments of 5G and IoT networks. Unlike conventional codes, these constructions allow enhanced structural flexibility that can be tuned for various application-specific parameters. While the potential relevance to quantum-safe communication is acknowledged, it is not the primary focus of this study. This work demonstrates how extending classical coding techniques into non-traditional algebraic domains opens up new directions for designing robust and efficient communication codes. Full article
(This article belongs to the Special Issue Mathematics for Algebraic Coding Theory and Cryptography)
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