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 giv-en 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 op-timal 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.