# Revision history [back]

### irreducible polynomial defining the finite field

X = GF(2).polynomial_ring().gen()

F = GF(28, name="a", modulus=X8 + X6 + X5 + X + 1)

As example above, the polynomial X8 + X6 + X5 + X + 1 is one of irreducible polynomial defining the finite field GF(28).

How can I get all the irreducible polynomial which can define the finite field GF(2**8)?

### irreducible polynomial defining the finite field

X = GF(2).polynomial_ring().gen()

F = GF(28, GF(2^8, name="a", modulus=X8 modulus=X^8 + X6 X^6 + X5 X^5 + X + 1)

As example above, the polynomial X8 X^8 + X6 X^6 + X5 X^5 + X + 1 is one of irreducible polynomial defining the finite field GF(28).GF(2^8).

How can I get all the irreducible polynomial which can define the finite field GF(2**8)?

### irreducible polynomial defining the finite field

X = GF(2).polynomial_ring().gen()

F = GF(2^8, name="a", modulus=X^8 + X^6 + X^5 + X + 1)

As example above, the polynomial X^8 + X^6 + X^5 + X + 1 is one of irreducible polynomial defining the finite field GF(2^8).

How can I get all the irreducible polynomial which can define the finite field GF(2**8)?GF(2^8)?