Modified genetic algorithms for constructing new quaternary hermitian LCD codes

Abstract

We propose two systematic methods for an efficient construction of quaternary Hermitian linear complementary dual (LCD) codes using two algorithms, called Iteration Search Algorithms I and II, which are modified genetic algorithms. Our algorithms include operators such as mutation, crossover, modified crossover, and complement to make the search space more effective. Using our algorithms, we obtain many new quaternary Hermitian LCD codes with best known minimum distances, including at least 133 such codes with several parameters, which are verified to be inequivalent to the currently known codes. Our methods demonstrate significantly efficient complexity in finding quaternary Hermitian LCD codes, contributing to the expansion of the current database for quaternary Hermitian LCD codes. © 2025 Elsevier B.V.