线性弱等重码的结构分析

线性弱等重码的结构分析 Structure Analysis of Linear Weak-Constant Weight Codes 袁媛 YUAN Yuan 1 first-author 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University C是二元[n,k,d]线性弱等重码,证明C等价于1阶Reed Muller码RM（k-1,1）的重复码.另外,根据已知结论,简洁证明了当C为二元[n,k,d]线性等重码,且C的码矩阵的列向量不为零向量时,C等价于极长码[2k-1,k,2k-1]的重复码. C is a binary linear weak-constant weight code, we show that C is equivalent to the repeated code of the first order Reed-Muller code RM（k-1,1）. Furthermore, by using some elemental calculation, we reprove that a constant weight code over binary field F 2 is equivalent to the repeated code of the maximal projective code over F 2 . 线性等重码 线性弱等重码 极长码 Reed-Muller码 linear constant weight codes linear weak-constant weight codes simplex codes Reed-Muller codes O157.4 国家基础科学发展计划（973计划）基金资助项目 2003-05-01 2021-04-01 5