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Well, we start with a small definition of XOR for bit strings larger than zero bits. $x$ and $y$ are bit strings with the lenght $n$ and $x_{k}$ denoting the $k^{th}$ bit (from $0$ to $lenght - 1$). $||$ represents concatenation and $\oplus$ means XOR. So we get: $$ x \oplus y = ((x_{0} \oplus y_{0}) || (x_{1} \oplus y_{1}) || ... || (x_{n-1} \oplus ...

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