Construction of irreducible polynomials over finite fields

Irreducible polynomials over finite fields and their applications have been quite well studied. Here, we discuss the construction of the irreducible polynomials of degree 4n over the finite field F(2)s for a given irreducible polynomial of degree n. Furthermore, we construct the irreducible polynomials of degree p(2)n over the finite field F(p)s for a given irreducible polynomial of degree n by using the method of composition of polynomials with some conditions on coefficients and degree of a given irreducible polynomial.