This paper introduces a class of Hermitian LCD 2-quasi-abelian codes over finite fields and presents a comprehensive enumeration of these codes in which relative minimum weights are small. We show that such codes can achieve asymptotically good over finite fields. Furthermore, we extend our analysis to finite chain rings by characterizing 2-quasi-abelian codes in this setting and proving the existence of asymptotically good Hermitian LCD 2-quasi-abelian codes over finite chain rings as well.
Bhowmick et al. (Sat,) studied this question.