线性弱等重码的结构分析

Structure Analysis of Linear Weak-Constant Weight Codes

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.