Recurrent methods for constructing irreducible polynomials over Fq of odd characteristics

In this paper, the irreducibility of the composition of polynomials with n 1 being the degree of P(x) Fq[x] is considered. Furthermore, some recurrent methods for constructing families of monic irreducible (including self-reciprocal) polynomials of degree n2k(k=1,2,3,…) over a finite field of odd characteristics is given.