On explicit factors of cyclotomic polynomials over finite fields
We study the explicit factorization of 2 (n) r-th cyclotomic polynomials over finite field F-q where q, r are odd with (r, q) = 1. We show that all irreducible factors of 2 (n) r-th cyclotomic polynomials can be obtained easily from irreducible factors of cyclotomic polynomials of small orders. In particular, we obtain the explicit factorization of 2 (n) 5-th cyclotomic polynomials over finite fields and construct several classes of irreducible polynomials of degree 2 (n-2) with fewer than 5 terms.
factorization cyclotomic polynomials finite fields irreducible polynomials dickson polynomials