deletions | additions       diff --git a/bits3.tex b/bits3.tex  index 9ace642..8e595a4 100644  --- a/bits3.tex  +++ b/bits3.tex 
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Verify that $x^4 + x^3 + x^2 + x + 1$ is not primitive via a LFSR.  \end{Exercise}  The polynomials in $\Fb[x]$ are infinite.  We observed that thanks describe a way  to make it finite and bounded by  a polynomial certain degree through a "polynomial relation". For example fix the  relations like to be  $x^3=x+1$ we as in the example above. We  can limit the number of elements in $\Fb[x]$ in this way: each time we find a monomial of degree greater than or equal to $3$ we substitute $x^3$ by $x+1$. At the end of this process we obtain a new polynomial of degree strictly less than $3$. For example  \[  \Fb[x], x^4+x^2=x(x^3)+x^2=x(x+1)+x^2=x^2+x+x^2=x.  \]  in this way: each time we find a monomial of degree greater than or equal to $3$ we substitute $x^3$ One can obtain the same result dividing the polynomial $x^4+x^2$  by$x+1$. At  theend of this process we obtain a new  polynomial of degree strictly less than $3$. That $x^3+x+1$. The remainder is $x$.  Hence the polynomials defined in the set  \[  \Fb[x], \mbox{ where }x^3=x+1  \]  are the polynomials \[  0, 1, x, x+1, x^2, x^2+x, x^2+1, x^2+x+1.   \] 
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where $a_2,a_1,a_0\in \Fb$.  For example we observed that