May 14, 2016 · The cyclotomic polynomial \(\Phi _n(x)\) is irreducible over \(\mathbb {F}_q\) if and only if n is equal to 2, 4, \(r^k\) or \(2r^k\), where r ...

In this paper, we study the factors of the cyclotomic polynomial Q2n.7(x) over finite field Fq when q ≡ ±1,±2,±3(mod 7) as an extension of [ ...

Explicit factorizations, into a product of irreducible polynomials, over Fq of the cyclotomic polynomials Q2n (x) are given in [4] when q ≡ 1 (mod 4).

In particular, we obtain the explicit factorization of 2n5-th cyclotomic polynomials over finite fields and construct several classes of irreducible polynomials ...

Nov 22, 2010 · We study the explicit factorization of 2^nr-th cyclotomic polynomials over finite field \mathbb{F}_q where q, r are odd with (r, q) =1.

Nov 7, 2012 · Those factorisations follow the factorisation of Φn on intermediate fields between Q and Q(ζn). For example, let n=12. There are 4 cases :.

Let q be a prime power and let Fq be a finite field with q elements. This paper discusses the explicit factorizations of cyclotomic polynomials over Fq.

Dec 30, 2019 · If a cyclotomic polynomial is reducible over a finite field, what does its factorisation look like? 2 · Representation of cyclotomic polynomial ...

This work describes a decisional attack against a version of the PLWE problem in which the samples are taken from a certain proper subring of large ...

Oct 22, 2024 · We study the explicit factorization of 2n r-th cyclotomic polynomials over finite field F q {\mathbb{F}_q} where q, r are odd with (r, ...