Research On Some Properties Of Constacyclic Codes

Constacyclic codes is an important class of linear codes.In this dissertation,the following two properties of constacyclic codes are studied:一、The depth distribution of constacyclic codes of length2^eoverΖ₄is studied.Firstly,the depth distribution of negacyclic codes of length2^eoverΖ₄is completely determined.Secondly,we determine the depth spectrum of cyclic codes of length2^e overΖ₄,and the depth distribution of some cyclic codes of length2^eoverΖ₄is also given.二、A class of constacyclic codes over the finite field（37）_q2of length （q^{2 m}-1）（q²-1）is studied.Firstly,by using cyclotomic cosets,the dimension of this class of constacyclic codes is determined.Secondly,a necessary and sufficient condition for this class of constacyclic codes to be Hermitian dual-containing codes and its application to quantum codes are given,quantum codes obtained have much bigger dimension than those quantum BCH codes in[32]and[33].Finally,by using this class of constacyclic codes,a class of entanglement-assisted quantum codes is also obtained.