Construction Of Entanglement Assisted Quantum Error-Correcting MDS Codes

Entanglement assisted quantum error-correcting code can boost the efficiency of information transmission and protect information from quantum noise during transmission.Recently,the construction on entanglement assisted quantum error-correcting MDS code has attracted the attention of many research.It is proposed that entanglement assisted quantum error-correcting code can be constructed by clas-sical linear codes.However,the parameters of the known results are still very lim-ited.In this thesis,we constructed two classes of entanglement-assisted quantum error-correcting MDS codes,our results have lengths q2+1/t and q2-1/h.Compared to some known results,the length can be any factor of q2±1 In the two constructions,we proposed a new approach on the decomposition of the defining set.According to this approach,the length of our codes are more general.Our results not only cover part of the known results but also innovate on the basis of the original results.In previous literature,the restriction that the denominator of the code length is a fixed constant,the problem can be solved by our approach.Hence we have more flexible code length and more codes can be constructed.