We study the explicit factorization of 2nr -th cyclotomic polynomials over finite field Fq where q, r are odd with (r, q) = 1. We show that all irreducible factors of 2nr -th cyclotomic polynomials can be obtained easily from irreducible factors of cyclotomic polynomials of small orders. In particular, we obtain the explicit factorization of 2n5-th cyclotomic polynomials over finite fields and construct several classes of irreducible polynomials of degree 2n-2 with fewer than 5 terms.

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Keywords Cyclotomic polynomials, Dickson polynomials, Factorization, Finite fields, Irreducible polynomials
Persistent URL dx.doi.org/10.1007/s10623-011-9537-6
Journal Designs, Codes and Cryptography
Wang, L. (Liping), & Wang, Q. (2012). On explicit factors of cyclotomic polynomials over finite fields. Designs, Codes and Cryptography, 63(1), 87–104. doi:10.1007/s10623-011-9537-6