几类最优重根循环码的构造  

On the Construction of Several Classes of Optimal Repeated-Root Cyclic Codes

作　　者：黄素娟[1,2] 孙中华 朱士信[1,2] HUANG Su-juan;SUN Zhong-hua;ZHU Shi-xin(School of Mathematics,Hefei University of Technology,Hefei,Anhui 230601,China;Intelligent Interconnected Systems Laboratory of Anhui Province(Hefei University of Technology),Hefei,Anhui 230009,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601 [2]智能互联系统安徽省实验室,安徽合肥230009

出　　处：《电子学报》2022年第1期142-148,共7页Acta Electronica Sinica

基　　金：国家自然科学基金(No.62002093,No.61772168,No.61802102);中央高校基本科研业务费专项资金资助(No.JZ2020HGQA0154,No.JZ2020HGTA0079,No.PA2019GDZC0097)。

摘　　要：本文分析了重根循环码的纠错能力.利用循环码的代数结构,构造了几类最优的循环码.构造了一类距离最优的二元重根循环码,并由此派生出一类距离和维数都是最优的二元重根循环码;构造了一类距离和维数都是最优的非二元重根循环码;构造了两类距离最优的非二元循环码.This paper analyzes the error-correction ability of repeated-root cyclic codes.By using the algebraic struc⁃ture of cyclic codes,several classes of optimal cyclic codes are constructed.A class of binary repeated-root cyclic codes with optimal distances is constructed,and then a class of binary repeated-root cyclic codes with optimal distances and di⁃mensions is derived;A class of non-binary repeated-root cyclic codes with optimal distances and dimensions is constructed;Two classes of non-binary cyclic codes with optimal distances are constructed.

关 键 词：重根循环码 最优码 HAMMING距离 

分 类 号：TN911.[电子电信—通信与信息系统]