A Family of Constacyclic Codes over ■2m+u■2mand Its Application to Quantum Codes

作     者：TANG Yongsheng YAO Ting ZHU Shixin KAI Xiaoshan 

作者机构：School of Mathematics and Statistics Hefei Normal University School of Mathematics Hefei University of Technology 

出 版 物：《Chinese Journal of Electronics》 (电子学报(英文))

年 卷 期：2020年第29卷第1期

页      面：114-121页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：supported by the Natural Science Foundation of Anhui Province(No.1808085MA15) Key University Science Research Project of Anhui Province(No.KJ2018A0497,No.KJ2018A0584) National Natural Science Foundation of China(No.61772168,No.61572168) 

主　　题：Constacyclic codes Cyclic codes Quasicyclic codes Gray map Quantum codes 

摘      要：Let R be the ring ■2m+u■2m,where u2=*** introduce a Gray map from R to ■2～2 m and study（1+u）-constacyclic codes over *** is proved that the image of a（1+u）-constacyclic code length n over R under the Gray map is a distance-invariant binary quasicyclic code of index m and length 2 *** also prove that every code of length 2 mn which is the Gray image of cyclic codes over R of length n is permutation equivalent to a binary quasi-cyclic code of index ***,a family of quantum error-correcting codes obtained from the Calderbank-Shor-Steane（CSS） construction applied to（1+u）-constacyclic codes over R.