Construction Of Quantum Codes Based On Constacyclic Codes Over Two Kinds Of Finite Rings

Quantum error correction plays an important role in the development of quantum communication.As a part of classical error-correcting codes,constacyclic codes have important theoretical significance.Quantum error-correcting codes have also attracted the attention of some scholars because of their applications in quantum communication.This thesis introduces the construction of quantum error-correcting codes by using constacyclic codes on rings,which is mainly divided into the following two parts:(1)Quantum codes are constructed by using constacyclic codes on the finite non-chain ring Fq+uFq+vFq+uvFq,where u2=u,v2=v,uv=vu and q=pm,p?3 is a prime,m is a positive integer.The properties of the ring are studied.A Gray mapping from R to Fq4 is introduced.Conditions for linear codes over R to be self-orthogonal are given.It is proved that some classes of constacyclic codes over R can be decomposed into different combinations of cyclic codes and negative cyclic codes.These constacyclic codes are used to construct quantum codes.Some quantum codes whose parameters are improved on minimum distance,dimension,and code rate are obtained.(2)Quantum codes are constructed by using cyclic codes on the ring Fp+uFp,where u2=1.The properties of the ring Fp+uFp are studied firstly.Then a distance preserving and self preserving orthogonal Gray mapping is established.Finally,we obtain some quantum codes with new parameters.