Exhaustive 
Here are exhaustive tables of irreducible polynomials with their orders over GF(2) for small degrees. 
LowSubDeg 
The form of these polynomials is P(x)=x^{d}+f(x)
with f(x) a polynomial of small degree. For a given degree d, the given polynomial is those of smallest subdegree deg(f(x)). 
Primitive 
Here are exhaustive tables of primitive polynomials over GF(2) for small degrees. 
PrimitiveTri 
The form of these primitive polynomials is P(x)=x^{d}+x^{n}+1
with n < d, and d a Mersenne number. This last property ensures that 2^{d}1 is a prime number, and therefore all irreducible polynomials of degree d are primitive.

Tables 
Here are NON exhaustive tables of primitive polynomials over GF(2) for degrees larger than 26. These polynomials were taken at random and checked whether primitive. These smaller tables than the exhaustive ones should be used when a small amount of primitive polynomials is needed.

Trinomials 
The form of these polynomials is P(x)=x^{d}+x^{n}+1
with n < d.
