TITLE: Finding the order of elements in a Galois Field
QUESTION [1 upvotes]: Does there exist a Galois field GF(4)?
GF(4)={0,1,2,3};
If we take this Galois field, then the element '2' is not having any degree..?
So is it possible to construct GF(4) ?

REPLY [1 votes]: Note that a polynomial over the field with 2 elements has a binary representation (technically this should be called "$x$-adic notation", since you're writing the polynomials in base $x$). In some contexts, it is understood that when we write an integer, that we mean the polynomial that has the same binary representation: e.g. $2$ means $x$ and $3$ means $1+x$.
(in my opinion, this is usually a bad convention)
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