| Entanglement assisted quantum codes are a kind of important error-correction codes that have attracted much attention in recent years.It makes full use of the entanglement resources shared in advance between the senders and the receivers to improve the information transmission rates.The most importantace of task is to study entanglement-assisted quantum codes in the quantum information and quantum communication.It is possible to construct an entanglement-assisted quantum error correcting(EAQEC)codes from any classical linear codes.However,the parameter of ebits C is usually calculated by computer search.Since the scope of computer search is limited and the search results are uncertain,we hope to determine the size of C by algebraic method.Firstly,in this thesis,we construct a class of[[2n-k,k,≥;c]]_q EAQEC codes by making some changes to the parity-check matrixs of classical linear codes from arbitrary binary or nonbinary[n,k,d]_q linear codes,where the parameter of ebits c=2n-2k can be easily determined by algebraic method.Secondly,we can obtain a new class of entanglement-assisted quantum codes based on GRS codes whoes lengths are given,where the parameter of ebits c can be easily generated algebraically.The constructed two classes of EAQEC codes are maximal-entanglement EAQEC codes.Finally,a class of entanglement-assisted quantum codes with parameters[[n+l,k-h,d’;n-k-h+l]]_q are constructed by using an orthogonal basis of the linear complementary dual(LCD)linear subcode of the classical linear code C with parameters[n,k,d]_q over a finite field F_q,where h=dim(Hull_E(C)),0≤l≤k-h,d≤d’≤d+l.In particular,when the classical linear code C is an Euclidean dual-containing linear code,there are entanglement-assisted quantum codes with parameters[[n+l,2k-n,d’;l]]_q,where 0≤l≤2k-n,d≤d’≤d+l.The research results mentioned above generalize and improve the previous research work,and hope to be helpful to the research of entanglement-assisted quantum codes in the future. |
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