基于常循环码的纠缠辅助量子Maximum-Distance-Separable码的构造  

Some New Families of Entanglement-Assisted Quantum Maximum-Distance-Separable Codes Constructed from Constacyclic Codes

作　　者：刘航宇 王立启[1] LIU Hangyu;WANG Liqi(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2024年第4期7-16,共10页College Mathematics

基　　金：国家自然科学基金(12271137)。

摘　　要：纠缠辅助量子纠错码可以看作是经典量子纠错码的引申,其与经典量子纠错码的差别在于,如果发送者和接收者双方提前共享纠缠态,在不满足对偶包含的的情况下也可以由任意经典线性码构造出来.本文通过研究分圆陪集的结构性质,利用常循环码构造出几类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 can be seen as a new-type of quantum error-correcting codes,unlike quantum error-correcting codes,it can be constructed from arbitrary linear codes by utilizing shared entangled states between the sender and the receiver in advance,even if it does not satisfy the dual-containing condition.Based on the structural properties of cyclotomic cosets,some new classes of entanglement-assisted quantum maximum-distance-separable(MDS)codes are constructed from constacyclic codes by exploiting small pre-shared entangled states.

关 键 词：纠缠辅助量子纠错码 常循环码 分圆陪集 MDS码 

分 类 号：O177.5[理学—数学]