Factorization of polynomial x^n-1 over finite fields

Abstract:

Factorization of the polynomial x^n-1 over finite fields is not only important theoretically, but also has a lots of applications, especially in secure communication and error-correcting coding theory. In this paper, an explicit factorization of x^n-1 into irreducible factors over the field F_q is given when ord_{rad(n)}q=2w, where w is an odd prime number. These results improve and generalize some recent progresses.