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I am trying to find the frame check sequence in cyclic redundancy check(CRC). Given that the generator polynomial is $\ g(x)= (x+1)(x^3 + x^2 + 1)$. Let's say the data sequence is $\ 10110001$.

In this case, $\ g(x) = x^4+x^3+x+x^3+x^2+1 $ after multiplying. But how do I handle 2 $\ x^3 $ terms? Is it okay to convert it into binary without worrying about it? For example, $\ 1 1111$ and continue with the division?

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When computing CRC, we are working over the field of two elements. In this field, 2=0. Therefore $$ (x+1)(x^3+x^2+1) = x^4+x^2+x+1. $$

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