On the Computation of the Automorphisms Group of Some Optimal Codes Using Genetic Algorithm

El Mehdi Bellfkih, Said Nouh, Imrane Chems Eddine Idrissi, Khalid Louartiti, Jamal Mouline


Many research papers in coding theory have recently focused on designing high-rate codes or improving codes that exist through a better understanding and then improving the coding and decoding algorithm. As a result, this paper aims to investigate the computation of the Automorphisms groups of some optimal codes (e.g., some linear circulant codes where their distance meets the lower bound and nonlinear Nordstrom-Robinson (24, 28, 6) code). These Automorphisms groups provide information about the structure of the code, which aids in both the design and enhancement and improvement of decoding algorithms. A new genetic algorithm-based method is proposed, with a detailed description of its components, the fitness function, selection, crossover, and mutation, and is used to find an important collection of Automorphisms; the results obtained have shown that the proposed method is effective in finding stabilizers set for some types of codes.


Keywords: automorphism group, optimal codes, genetic algorithm, crossover, mutation.




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