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

Abstract

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.

Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices

“…GA offers several advantages over traditional algorithms: It relies solely on the objective function's evaluation, irrespective of its characteristics (e.g., continuity, and differentiability), providing greater flexibility and applicability across diverse problem domains [20,21].…”