Genetic Algorithm-Based Approach for Discovering Involutory MDS Matrices

In this paper, we present an innovative approach for the discovery of involutory Maximum Distance Separable (MDS) matrices over finite fields F2q , derived from MDS self-dual codes, by employing a technique based on genetic algorithms. The significance of involutory MDS matrices lies in their unique properties, making them valuable in various applications, particularly in coding theory and cryptography. We propose a genetic algorithm-based method that efficiently searches for involutory MDS matrices, ensuring their self-duality and maximization of distances between code words. By leveraging the genetic algorithm's ability to evolve solutions over generations, our approach automates the process of identifying optimal involutory MDS matrices. Through comprehensive experiments, we demonstrate the effectiveness our method. The proposed approach opens up new possibilities for practical applications, as well as potential extensions to related problems in coding theory and cryptographic systems.