Construcrting Quantum MDS Code Based On Constacyclic Codes

Quantum error correcting codes play an important role in quantum information and quantum computation,and can overcome the decoherence of quantum systems and the environment.If a quantum code satisfies n=k+2d-2.then it is called quantum MDS code with strong error correction capability.Recently,constructing quantum MDS codes has become a hot topic of discussion academy.In this paper,the quantum MDScode with the form n=(q~2+1)/a is constructed by using the Hermitian construction method based on the classical cyclic code,where q=2am+t and a |(t~2+1).The main research contents are as follows:(?)Finding the definition set of the cyclic code C,then we prove C?H(?)C by using properties of the cyclotomic coset and the skew symmetric cyclotomic coset.(?)Letting r=2 and r=q+1,where r=ord(?),we construct two new classes of quantum MDS codes by using the Hermitian construction method and constacyclic code over Fq2.