| Quantum error-correcting codes are widely applied in quantum information the-ory and quantum computation.Similarly to classical error-correcting codes,error-correcting capability of quantum codes is an essential impact to ensure the validity of quantum communication and quantum computation.In what follows,quantum maximum-distance-separable(MDS)codes with good error-correcting capability are an important class of quantum codes.In recent years,many scholars have used known classical error-correcting codes such as Reed-Muller codes,BCH codes,alge-braic geometry codes,constacyclic codes to construct quantum MDS codes with good parameters,and the commonly-used methods of constructing quantum MDS codes are CSS construction,Steane construction and Hermitian construction.In this the-sis,we introduce the basic definitions and results of quantum MDS codes,Hermitian dual codes and constacyclic codes,and apply Hermitian construction and classical constacyclic codes to construct two classes of quantum MDS codes.One is of length q2-1/2t1t2,some of which have new lengths.The other class is of length q2+1/10.which has been constructed in[10]and[13]by using cyclic codes.However,our tool is consta-cyclic codes.Compared with the work of[10]and[13],our method is simpler and shorter. |
