基于广义Reed-Solomon码构造的两类量子MDS码

Two Classes of Quantum MDS Codes from Generalized Reed-Solomon Codes

量子信息领域的一个重要热点是构造具有良好参数的量子极大距离可分码.最小距离是其中最重要的一个参数,并且最小距离越大越好,在量子纠错领域一个备受关注的话题是构造最小距离比q/2+1更大的量子极大距离可分码.构造了向量a和向量v,使得由向量a和向量v定义的广义Reed-Solomon码满足Hermite自正交性质.进一步,利用Hermite构造法证明了两类量子极大距离可分码存在.构造的大多数量子极大距离可分码的最小距离比q/2+1大.

The construction of quantum maximum distance separable codes with good parameters is an important hotspot in the field of quantum information theory.The minimum distance is one of the most important parameters,and the code performs better if it has a larger minimum distance.Amajor concern today is to construct quantum MDDS codes with minimum distance bigger than q/2+1.Construct some vectors a and v,such that the generalized ReedSolomon codes defined by a and v are Hermitian self-orthogonal.Furthermore,it is shown that two classes of quantum MDS codes exist by the classical Hermitian construction method.Most of quantum MDS codes in this paper have minimum distance larger than q/2+1.