二元广义反码与最优LCD码  

Binary Generalized Anti-Code and Optimal LCD Code

作　　者：李瑞虎[1] 付强[1] 宋昊[1] 刘杨 LI Ruihu;FU Qiang;SONG Hao;LIU Yang(Department of Basic Sciences,Air Force Engineering University,Xi’an 710051,China)

机构地区：[1]空军工程大学基础部,西安710051

出　　处：《空军工程大学学报》2024年第1期123-127,共5页Journal of Air Force Engineering University

基　　金：国家自然科学基金(U21A20428);陕西省自然科学基础研究计划(2022JQ046)。

摘　　要：基于二元线性码的定义向量理论,引入广义反码及其定义向量概念,确立广义反码、它的参数与二元最优线性码之间的联系。利用广义反码的性质和参数研究对应二元最优线性码的线性补对偶(LCD)性质,证明11类二元最优线性码不是LCD码。该方法突破现有方法的局限性,为研究高维二元LCD的参数确定与构造问题提供了可借鉴的新理论和新方法。Based on the defining vector of binary linear code,new concept of generalized anti-code of a given code is introduced into this paper,and the defining vector of a generalized anti-code is described by the given code.The parameters of a generalized anti-code are utilized for determining corresponding binary optimal code.It is proved that 11 classes of binary optimal codes are not LCD codes.And such method breaks through the limitations of the current methods,and provides a new theory and a new method for study of LCD parameters determination and structure.

关 键 词：广义反码 线性补对偶码 定义向量 最优码 

分 类 号：O157.4[理学—数学]