矩阵计算帮我们找到群码 Define the null space of a matrix H∈Mmxn(Z2） to be the set of all binary n-tuples x such that Hx=0.We denote the null space of a matrix H by Null(H). Theorem 8.6 Let H be in Mmxn(Z2).Then the null space of H is a group code. PROOF.Since each element of Z2 is its own inverse,the only thing that really needs to be checked here is closure.Let x,y e Null(H)for some matrix H in Mmxn(Z2).Then Hx =0 and Hy =0.So H(x+y)=H(x+y)=Hx+Hy=0+0=0. Hence,x+y is in the null space of H and therefore must be a codeword.矩阵计算帮我们找到群码