# About the irreducible test for a polynomial over $GF(2^m)$ (its coefficients belong to $GF(2^m)$)

For the Miller-Rabin probabilistic primality test, we can apply it to test a big number whether a probably prime number or not. Does there exist a method to test a higher-degree polynomial over $$GF(2^m)$$ whether it is an irreducible polynomial or not? Note that the coefficients of the polynomial belong to $$GF(2^m)$$.

This problem has been solved. Thanks the help from kelalaka.