PSO-Guided Construction of MRD Codes for Rank Metrics.
Saved in:
| Title: | PSO-Guided Construction of MRD Codes for Rank Metrics. |
|---|---|
| Authors: | Dehghani, Behnam, Sakhaie, Amineh |
| Source: | Mathematics (2227-7390); Sep2025, Vol. 13 Issue 17, p2756, 13p |
| Subject Terms: | ERROR-correcting codes, PARTICLE swarm optimization, SWARM intelligence, FINITE fields, ENCODING |
| Abstract: | Maximum Rank-Distance (MRD) codes are a class of optimal error-correcting codes that achieve the Singleton-like bound for rank metric, making them invaluable in applications such as network coding, cryptography, and distributed storage. While algebraic constructions of MRD codes (e.g., Gabidulin codes) are well-studied for specific parameters, a comprehensive theory for their existence and structure over arbitrary finite fields remains an open challenge. Recent advances have expanded MRD research to include twisted, scattered, convolutional, and machine-learning-aided approaches, yet many parameter regimes remain unexplored. This paper introduces a computational optimization framework for constructing MRD codes using Particle Swarm Optimization (PSO), a bio-inspired metaheuristic algorithm adept at navigating high-dimensional, non-linear, and discrete search spaces. Unlike traditional algebraic methods, our approach does not rely on prescribed algebraic structures; instead, it systematically explores the space of possible generator matrices to identify MRD configurations, particularly in cases where theoretical constructions are unknown. Key contributions include: (1) a tailored finite-field PSO formulation that encodes rank-metric constraints into the optimization process, with explicit parameter control to address convergence speed and global optimality; (2) a theoretical analysis of the adaptability of PSO to MRD construction in complex search landscapes, supported by experiments demonstrating its ability to find codes beyond classical families; and (3) an open-source Python toolkit for MRD code discovery, enabling full reproducibility and extension to other rank-metric scenarios. The proposed method complements established theory while opening new avenues for hybrid metaheuristic–algebraic and machine learning–aided MRD code construction. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics (2227-7390) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Complementary Index |
Full Text Finder 
Nájsť tento článok vo Web of Science Be the first to leave a comment!