Construction Of Some Classes Of Entanglement-Assisted Quantum MDS Codes Over Finite Fields

In recent years,quantum information and quantum computing have become a hot topic,among which quantum error-correcting codes have attracted extensive attention.It is very important to construct,quantum error correcting codes with good parameters.In this area,entanglement-assisted quantum error-correcting codes have also attracted the attention of many researchers.A large number of entanglement-assisted quantum error-correcting codes that scholars have constructed mainly through generalized Reed-Solomon codes,constacyclic codes,negacyclic codes and so on.In this paper,four classes of entanglement-assisted quantum error-correcting codes based on the theory of constacyclic codes and generalized Reed-Solomon codes over finite fields are constructed.The main results of this dissertation can be summarized as follows:First,in Chapter 3,we construct two families of entanglement-assisted quantum error-correcting codes by constacyclic codes.Specific contents are as below:·[[q2+1/5,q2+1/5-6q-32/5-4τ,3q-1/5+2τ;4]]q,where q is an odd prime power with q≡-3(mod 10)andq+1/ris odd,1≤τ≤q+3/5.·[[q2+1/5,q2+1/5-6q-28/5-4τ,3q+1/5+2τ;4]]q,where q is an odd prime power with q≡3(mod 10)and q+1/r is odd,1<τ<q+2/5.Secondly,in Chapter 4,two classes of entanglement-assisted quantum error-correcting codes from generalized Reed-Solomon codes.Specific contents are as below:·[[n,n-2d+c+2,d;c]]q,where n=q2-1/2+(q2-1)/b,b|(q+1)and b≡ 2(mod 4),2 ≤d≤3(q+1)/4+q+1/2b and c=b/2.·[[n,n-2d+c+2,d;c]]q,where n=q2-1/2+2(q2-1)/b,q>3,b|(q+1)and b≡ 0(mod 4),2≤d≤3q-1/4+q+1/b and c=b/2+1.