In computer science the XOR operation is a very important one, and I've heard XOR referred to as a "linear" function. My experience with linear functions (in the sense of vector spaces) has only been with functions in one variable, but XOR is a function of two.(adsbygoogle = window.adsbygoogle || []).push({});

I know that we start by using the field [tex]F_2 = {0, 1}[/tex] in which addition is actually the XOR operation. So addition of two vectors from a vector space over that field (say, two 32-bit integers) is merely addition of the vectors using the field addition operation.

So then the XOR operation on 32-bit integers isn't a special function so much as it is really just addition of 32-dimension vectors over [tex]F_2[/tex]. So what is the definition for the addition of two elements in a field to be linear, and how does the (XOR) addition over [tex]F_2[/tex] qualify as linear?

I'm sure I've encountered these answers before, but I'm blanking at the moment. :-S

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# How does XOR qualify as a linear function?

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