Coding Theory and the Impact of AI

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 480

Special Issue Editors


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Guest Editor
School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Interests: algebraic coding theory; cryptographic functions; artificial intelligence

E-Mail Website
Guest Editor
School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Interests: reinforcement learning; multi-agent systems; multi-armed bandits

Special Issue Information

Dear Colleagues,

As digital computing and communication technologies advance at an unprecedented pace, securing the safety of communications and boosting their efficiency have become vital components of the Information Age landscape. This Special Issue devotes considerable attention to the forefront developments and future directions in research encompassing coding theory, cryptography, and information security. Its primary aim is to delve deeply into the foundational theoretical questions inherent in coding theory, fostering further study in mathematical theories that underpin error-correcting codes and cryptographic realms. Concurrently, it maintains a tight link with the extensive field of applied mathematics, investigating how coding theory and cryptography can be synergistically combined with emerging technologies in computer science to realize innovative applications across the domains of telecommunications and information security.

Dr. Yansheng Wu
Dr. Shangdong Yang
Guest Editors

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Keywords

  • coding theory
  • sequences
  • artificial intelligence
  • machine learning
  • cryptography
  • information security
  • data transmission

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Published Papers (1 paper)

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Research

14 pages, 271 KiB  
Article
On the Stability of the Linear Complexity of Some Generalized Cyclotomic Sequences of Order Two
by Chi Yan and Chengliang Tian
Mathematics 2024, 12(16), 2483; https://doi.org/10.3390/math12162483 - 11 Aug 2024
Viewed by 300
Abstract
Linear complexity is an important pseudo-random measure of the key stream sequence in a stream cipher system. The 1-error linear complexity is used to measure the stability of the linear complexity, which means the minimal linear complexity of the new sequence by changing [...] Read more.
Linear complexity is an important pseudo-random measure of the key stream sequence in a stream cipher system. The 1-error linear complexity is used to measure the stability of the linear complexity, which means the minimal linear complexity of the new sequence by changing one bit of the original key stream sequence. This paper contributes to calculating the exact values of the linear complexity and 1-error linear complexity of the binary key stream sequence with two prime periods defined by Ding–Helleseth generalized cyclotomy. We provide a novel method to solve such problems by employing the discrete Fourier transform and the M–S polynomial of the sequence. Our results show that, by choosing appropriate parameters p and q, the linear complexity and 1-error linear complexity can be no less than half period, which shows that the linear complexity of this sequence not only meets the requirements of cryptography but also has good stability. Full article
(This article belongs to the Special Issue Coding Theory and the Impact of AI)
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