Explicit Factorization of Cyclotomic Polynomials Over Finite Fields

Abstract

In this paper, we make an attempt to study the explicit factorization of 2 n .7-th cyclotomic polynomials over finite field F q when q ≡ 1(mod 4) into a product of distinct monic irreducible polynomials, where q is a power of an odd prime.

On the number of k-normal elements over finite fields

“…The case n = 2 m r in which q and r are odd with gcd(q, r) = 1 was studied in [16] and complete factorization for the case n = 2 m 5 for any odd characteristic field was settled. Complete factorization for the case n = 2 m 7 for any characteristic was given in [5]. The relationship between cyclotomic polynomials Q 2 m r and Q r was given in [15] where r and q are odd.…”