量子常循环码的构造研究  

Research on Construction of Quantum Constacyclic Codes

作　　者：朱士信[1] ZHU Shixin(School of Mathematics,Hefei University of Technology,Hefei 230601,Anhui)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601

出　　处：《四川师范大学学报（自然科学版）》2023年第5期569-580,F0002,共13页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(U21A20428)。

摘　　要：量子纠错码是实现量子通信和量子计算的有效编码方案,如何构造高性能的量子纠错码是量子纠错理论最基本的研究课题之一.量子常循环码具有良好的代数结构,可以通过量子线性移位寄存器进行编译,在未来量子通信系统中有着广泛的应用前景.本综述将介绍量子常循环码的构造方法,揭示经典常循环码与量子纠错码之间的联系,阐述经典常循环码在量子MDS码和纠缠辅助量子MDS码中的应用.Quantum error-correcting codes are an effective coding scheme that can realize quantum communication and computation.It is one of the most basic topics to construct quantum error-correcting codes with high error-correcting capability.Quantum constacyclic codes have good algebraic structure,which can be encoded and decoded by quantum linear shift register.Hence,they have wide application prospect in quantum communication system in the future.In this review paper,we introduce the methods of the construction of quantum constacyclic codes and reveal the relationship between classical constacyclic codes and quantum error-correcting codes.We mainly elaborate some applications of classical constacyclic codes to quantum MDS codes and entanglement-assisted quantum MDS codes.

关 键 词：常循环码 量子码 量子MDS码 纠缠辅助量子码 

分 类 号：O236.2[理学—运筹学与控制论]