  In this paper we consider in detail the composition of an irreducible
polynomial with X^2 and suggest a recurrent construction of irreducible
polynomials of fixed degree over finite fields of odd characteristics. More
precisely, given an irreducible polynomial of degree n and order 2^rt with t
odd, the construction produces ord_t(2)/d irreducible polynomials of degree n
and order t for a certain divisor d of n. The construction can be used, for
example, to search irreducible polynomials with specific requirements on its
coefficients.
