Research On Quaternary Hermitian LCD Codes And Hermitian Self-orthogonal Codes

Linear complementary dual codes(which is abbreviated to LCD codes)over finite fields have good structure and properties,and have been widely used in data storage and against dual channel attack.It is one of the hot research directions in coding theory.Self-orthogonal codes are a very important kind of codes in classical error-correcting codes.With the continuous development of quantum error-correction technology,it is found that classical self-orthogonal codes can be used to construct quantum error-correction codes,which arouses great interest of scholars in constructing classical self-orthogonal codes.This paper studies the Hermitian LCD codes and Hermitian self-orthogonal codes over finite fields,and focuses on the construction of the quaternary Hermitian LCD codes and Hermitian self-orthogonal codes,as well as the minimum distance of the quaternary Hermitian LCD codes.The main contents are as follows:(1)Based on the conditions for linear codes over finite fields to be Hermitian LCD codes,the maximum values of minimum distance of two-dimensional Hermitian LCD codes over quaternary fields with smaller code-length are given.Furthermore,the general rules that the maximum values of the minimum distance of the two-dimensional Hermitian LCD codes over the quaternary fields are studied.(2)According to the necessary and sufficient conditions for linear codes over finite fields to be Hermitian LCD codes or Hermitian self-orthogonal codes,four kinds of quaternary Hermitian LCD codes and Hermitian self-orthogonal codes are constructed by selecting the appropriate definition sets.At the same time,Hermitian dual codes of these four kinds of linear codes are studied and some quaternary optimal linear codes are also obtained.