1-Lee重量和2-Lee重量Z_(2)R_(2)[v]-加性码  

One-Lee Weight and Two-Lee Weight Z_(2)R_(2)[v]-Additive Codes

作　　者：刘家凤 施敏加[1] LIU Jiafeng;SHI Mingjia(School of Mathematical Sciences,Anhui University,Hefei 230601)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《系统科学与数学》2022年第8期2235-2244,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金面上项目(12071001)资助课题.

摘　　要：文章主要研究1-Lee重量和2-Lee重量Z_(2)R_(2)[v]-加性码的构造,其中R_(2)[v]=Z_(2)+vZ_(2)+v^(2)Z_(2)(v^)3_=v).通过定义一个从环R_(2)[v]到F^(3)_(2)的新的Gray映射,在这个新的Gray映射下我们给出了环R_(2)[v]中每个元素的Lee重量的定义,接着在此基础上讨论了在环Z_(2)R_(2)[v]上1-Lee重量和2-Lee重量加性码的结构性质.研究了1-Lee重量和2-Lee重量Z_(2)R_(2)[v]-加性码的构造方法,针对不同的构造方法,得到了具体的生成矩阵,并分析了在每种构造方法下得到的1-Lee重量和2-Lee重量码的重量分布.最后给出具体例子来说明文章的主要结论.This paper is devoted to the construction of one and two-Lee weight Z_(2)R_(2)[v]-additive codes,where R_(2)[v]=Z_(2)+vZ_(2)+v^(2)Z_(2)(v^(3)=v).By defining a new Gray map from the ring R_(2)[v]to F^(3)_(2),under this new Gray map we give a definition of the Lee weight of each element in the ring R_(2)[v],and then on this basis we discuss the structural properties of one-Lee weight and two-Lee weight additive codes on the ring Z_(2)R_(2)[v].The construction methods of one-Lee weight and two-Lee weight Z_(2)R_(2)[v]-additive codes are studied.For different construction methods,we obtain specific generating matrices and analyze the weight distributions of one-Lee weight and two-Lee weight codes obtained under each construction method.Finally,specific examples are given to illustrate our main conclusions.

关 键 词：加性码 1-Lee重量码 2-Lee重量码 生成矩阵 

分 类 号：O157.4[理学—数学]