Michela Ceria edited section_Bytes_The_polynomials_in__.tex  over 7 years ago

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\section{Bytes}  The polynomials in $\Fb[x]$ are infinite. We describe a way to make it finite and bounded by a certain degree through a "polynomial relation". For example fix the relations to be $x^3=x+1$, or equivalently $x^3+x+1=0$, 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  \[  x^4+x^2=x(x^3)+x^2=x(x+1)+x^2=x^2+x+x^2=x.