Constacyclic codes over finite fields are a class of important linear codes.This class of codes has rich algebra structure and its encoding and decoding circuits can be easily performed.Constacyclic codes over finite fields have many applications in information transmission.In this paper

the structure of Hermitian self-orthogonal constacyclic codes over a class of finite fields of any length is studied.By using generator polynomial

the condition for the existence of Hermitian self-orthogonal constacyclic codes over this class of finite fields is explored and the enumeration formula of such codes is determined.Further

Hermitian self-orthogonal constacyclic codes over this class finite fields are applied to construct some optimal quantum codes.