On LCD Constacyclic Codes Over Finite Fields

As an important subclass of linear codes,cyclic codes have excellent algebraic properties over finite fields,so they are well studied by researchers.Several special cyclic codes are obtained from the relationship between cyclic codes and their dual codes become a new research hotspot,such as self-dual cyclic code(C=C~?)and LCD cyclic code(C(?)C~?={0}).More generally,the cyclic codes can be generalized to the constacyclic codes.What's more,the dual contained constacyclic codes can be used to construct quantum codes.In this dissertation,we mainly study the following main content(1)The structure and properties of LCD negacyclic codes are studied over finite fields with length n by discussing the q-cyclotomic coset and generator polynomial of negacyclic codes,and the parameters of LCD negacyclic is obtained codes with length(?) and (?),and a large number of optimal LCD codes are obtained.(2)Two types of LCD MDS codes are constructed from the negacyclic codes over finite fields(3)The LCD repeated-root cyclic codes is studied over finite fields.The necessary and sufficient condition for the repeated-root cyclic codes is LCD code is given.(4)The minimum distance of the LCD repeated-root cyclic codes is studied over finite fields.Finally,the enumeration of LCD repeated-root cyclic codes of length n is given over finite fields.