Construction Of Several Linear Complementary Dual Codes And Corresponding Entanglement-assisted Quantum Codes

The development of computer and communication technology puts forward new re-quirements for algebraic coding theory.As a powerful tool in the theory of algebraic coding,the construction of codewords with good performance over finite fields has become a hot topic of research.Therefore,in this paper,we firstly construct several types of linear com-plementary dual codes,which have good parameters,such as q=3~m(m≥2).Secondly,the entanglement-assisted quantum code is constructed with these linear complementary dual codes,and the constructed quantum code reaches the entanglement-assisted quan-tum Singleton bound and the maximum entanglement-assisted quantity,The main results are as follows:(1)When q≡1(mod 4),the parameters of linear complementary dual code are:[(q~2-1)/4,n-δ-1,δ+2],the parameters of entanglement-assisted quantum code are:[[n,n-δ-1,δ+2;δ+1]]_q,(2)When q≡3(mod 4),(q≠3),the parameters of linear complementary dual code are:[(q~2-1)/4,n-δ-1,δ+2],the parameters of entanglement-assisted quantum code are:[[n,n-δ-1,δ+2;δ+1]]_q,(3)When q=3~m(m≥2),the parameters of linear complementary dual code are:[q~2+1,n-2δ-1,2δ+2],the parameters of entanglement-assisted quantum code are:[[n,n-2δ-1,2δ+2;2δ+1]]_q.