Genetic Algorithm-Based Method 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...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi-Wiley
2023-01-01
|
| Series: | Computational and Mathematical Methods |
| Online Access: | http://dx.doi.org/10.1155/2023/5951901 |
| _version_ | 1797363907104342016 |
|---|---|
| author | El Mehdi Bellfkih Said Nouh Imrane Chems Eddine Idrissi Khalid Louartiti Jamal Mouline |
| author_facet | El Mehdi Bellfkih Said Nouh Imrane Chems Eddine Idrissi Khalid Louartiti Jamal Mouline |
| author_sort | El Mehdi Bellfkih |
| collection | DOAJ |
| description | 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 of our method and also unveil essential insights into automorphism groups within MDS self-dual codes. These findings hold promise for practical applications and extend the horizons of knowledge in both coding theory and cryptographic systems. |
| first_indexed | 2024-03-08T16:27:41Z |
| format | Article |
| id | doaj.art-d1702487f931425ba9cf54c43b372d64 |
| institution | Directory Open Access Journal |
| issn | 2577-7408 |
| language | English |
| last_indexed | 2024-03-08T16:27:41Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi-Wiley |
| record_format | Article |
| series | Computational and Mathematical Methods |
| spelling | doaj.art-d1702487f931425ba9cf54c43b372d642024-01-07T00:00:03ZengHindawi-WileyComputational and Mathematical Methods2577-74082023-01-01202310.1155/2023/5951901Genetic Algorithm-Based Method for Discovering Involutory MDS MatricesEl Mehdi Bellfkih0Said Nouh1Imrane Chems Eddine Idrissi2Khalid Louartiti3Jamal Mouline4LAMSLTIMLTIMSMADLAMSIn 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 of our method and also unveil essential insights into automorphism groups within MDS self-dual codes. These findings hold promise for practical applications and extend the horizons of knowledge in both coding theory and cryptographic systems.http://dx.doi.org/10.1155/2023/5951901 |
| spellingShingle | El Mehdi Bellfkih Said Nouh Imrane Chems Eddine Idrissi Khalid Louartiti Jamal Mouline Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices Computational and Mathematical Methods |
| title | Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices |
| title_full | Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices |
| title_fullStr | Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices |
| title_full_unstemmed | Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices |
| title_short | Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices |
| title_sort | genetic algorithm based method for discovering involutory mds matrices |
| url | http://dx.doi.org/10.1155/2023/5951901 |
| work_keys_str_mv | AT elmehdibellfkih geneticalgorithmbasedmethodfordiscoveringinvolutorymdsmatrices AT saidnouh geneticalgorithmbasedmethodfordiscoveringinvolutorymdsmatrices AT imranechemseddineidrissi geneticalgorithmbasedmethodfordiscoveringinvolutorymdsmatrices AT khalidlouartiti geneticalgorithmbasedmethodfordiscoveringinvolutorymdsmatrices AT jamalmouline geneticalgorithmbasedmethodfordiscoveringinvolutorymdsmatrices |