一道编码理论里面的题目~Let x,y be codewords in a self-orthogonal binary code.Suppose the weights of x and y are both divisible by 4.Show that the weight of x + y is also a multiple of 4.

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一道编码理论里面的题目~Let x,y be codewords in a self-orthogonal binary code.Suppose the weights of x and y are both divisible by 4.Show that the weight of x + y is also a multiple of 4.

一道编码理论里面的题目~Let x,y be codewords in a self-orthogonal binary code.Suppose the weights of x and y are both divisible by 4.Show that the weight of x + y is also a multiple of 4.
一道编码理论里面的题目~
Let x,y be codewords in a self-orthogonal binary code.Suppose the weights of x and y are both divisible by 4.Show that the weight of x + y is also a multiple of 4.

一道编码理论里面的题目~Let x,y be codewords in a self-orthogonal binary code.Suppose the weights of x and y are both divisible by 4.Show that the weight of x + y is also a multiple of 4.
由于x,y都是二元码,有公式wt(x+y)=wt(x)+wt(y)-2wt(x*y),由于x,y同属于self-orthogonal binary code,所以,x*y=0,即：wt(x*y)=0;所以：wt(x+y)=wt(x)+wt(y),wt(x),wt(y)都能被4整除,左边也就也能被4整除.

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