The Construction Of A Class Of Quantum Codes

It is well-known that there is an inevitable interaction between the quantum states and the external environment.This action leads to decoherent of the quantum infor-mation.One of the most of powerful method to overcome quantum decoherence is to use quantum error correction codes.As a result,it becomes attractive for constructing quantum error correction codes.Based on the previous work,we use classical linear codes to construct a class of quantum error correcting codes in this thesis.And we improve the parameters of the new quantum error correction codes.We begin with the research background,the development and the interesting prob-lems of quantum error correcting codes.Then,we introduce some basic concepts of quantum error correcting codes and some basic knowledge which will be used.As we know,the classical linear codes is an important tool to study the quantum error correction codes,we study the length of the codes next.We improve the codes efficiency by shortening the code length.The Hermitian construction is a cut way to approach construction.Next we use a class of polynomials based on a normal basis to construct the classical linear codes whose parameters are new,which generalize the range of the parameter t.As a sequent,we construct a class of quantum error correcting codes by means of the Hermitian construction method and the new classical linear codes we found.The quantum codes we constructed extend the value range of the codes known.Cyclic codes and BCH codes are also two important classes classical linear codes.Finally,we study the quantum MDS codes after we introduce some basic concepts of them.Morover,we construct the quantum codes having the new parameter by the cyclic codes and prove the existence of quantum MDS codes when n=q2+1/2.The main method which we use is to find the corresponding elements x such that the elements contained in the set Z are continuous.