新纠缠辅助量子MDS码的构造  

Construction of New Entanglement-Assisted Quantum MDS Codes

作　　者：汪盼 王立启[1] 朱士信[1] WANG Pan;WANG Li-qi;ZHU Shi-xin(School of Mathematics,Hefei University of Technology,Hefei,Anhui 230000,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230000

出　　处：《电子学报》2024年第1期288-297,共10页Acta Electronica Sinica

基　　金：国家自然科学基金(No.12271137,No.U21A20428,No.12171134)。

摘　　要：纠缠辅助量子纠错码是经典量子纠错码的推广,通过在接收者和发送者双方预先共享纠缠态的方式实现量子通信.由于预先共享纠缠态会造成额外的费用,如何构造具有较小预先共享纠缠态的纠缠辅助量子纠错码是一个有趣的问题.本文给出了有限域Fq2上一类负循环码是厄米特对偶包含码的充分条件,通过研究其分圆陪集的结构性质,确定了不同数目的预先共享纠缠态的存在条件,并结合纠缠辅助量子纠错码的构造方法,构造了一些新的具有较小预先共享纠缠态的纠缠辅助量子Maximum-Distance-Separable(MDS)码.Entanglement-assisted quantum error-correcting codes are the generalization of classical quantum error-correcting codes,which realize quantum communication by using pre-shared entangled states between the receiver and the sender.It is an interesting problem to construct entanglement-assisted quantum error-correcting codes with small pre-shared entangled states because of the extra cost of pre-shared entangled states.In this paper,a sufficient condition for a class of negacyclic codes over finite fields to be Hermitian dual-containing codes is given.Then based on the structural properties of cyclotomic cosets,the existence conditions of different number of pre-shared entangled states are determined,and some new entanglement-assisted quantum maximum-distance-separable(MDS)codes with small pre-shared entangled states are obtained by using the construction method of entanglement-assisted quantum error-correcting codes.

关 键 词：分圆陪集 负循环码 纠缠辅助量子纠错码 MDS码 

分 类 号：O157.4[理学—数学] TN911.22[理学—基础数学]