Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) from Calderbank-Shor-Steane (CSS) construction. In general, it's difficult to determine the required number of maximally entangled states of an AEAQECC, which is associated with the dimension of the intersection of the two corresponding linear codes. Two linear codes are said to be a linear l-intersection pair if their intersection has dimension l. In this paper, all possible linear l-intersection pairs of MDS codes are given. As an application, we give a complete characterization of pure MDS AEAQECCs for all possible parameters.
翻译:最近,Galindo等人从Calderbank-Shor-Steane(CSS)的构造中引入了不对称缠绕辅助量子错误校正代码的概念,一般来说,很难确定AEAQECC的最大缠绕状态的所需数量,这与两个相应的线性代码的交点维度相关。如果两条线性代码的交叉点具有维度,则两条线性代码被称为线性一对线性一对。本文给出了所有可能的MDS代码的线性一对线性一对。作为应用,我们给出了所有可能的参数的纯MDS AEAQC的完整特征描述。