The weight distributions and weight hierarchies of two classes of self-orthogonal codes

Self-orthogonal codes, a specialized subclass of linear codes contained within their dual codes, are of significant interest in coding theory. Investigating their weight distributions and weight hierarchies constitutes a key research area, as these properties provide crucial structural insights into the codes and fundamentally impact their performance in practical applications. Nevertheless, determining the weight distributions and generalized Hamming weights of self-orthogonal codes, particularly the Hamming weights hierarchies, remains a challenging problem. Few established results currently exist on the Hamming weights hierarchies of self-orthogonal codes. In this paper, two classes of self-orthogonal codes are constructed by defining sets. For these codes, we explicitly determine both their weight distributions and their weight hierarchies. Notably, according to the tables of best known codes maintained in [7], some of the constructed codes are optimal.