Constacyclic codes over finite fields are a class of important linear codes.This class of codes has rich algebra tructure and its encoding and decoding circuits can be easily performed.Constacyclic codes over finite fields have any 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.%有限域上常循环码具有丰富的代数结构,其编译码电路容易实现,因而在信息传输实践中具有重要的应用.该文研究了一类有限域上任意长度的厄米特自正交常循环码的结构,给出了此类有限域上厄米特自正交常循环码的生成多项式与存在条件,确立了此类有限域上厄米特自正交常循环码的计数公式,并且利用此类有限域上偶长度的厄米特自正交常循环码构造了最优的量子码.
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