The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

Abstract Swan (Pac. J. Math. 12: 1099–1106, 1962) gives conditions under which the
trinomial xn+ xk+ 1 over F _ 2 is reducible. Vishne (Finite Fields Appl. 3: 370–377, 1997) …

Formulas for cube roots in F3m - ScienceDirect Skip to main contentSkip to article Elsevier logo
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Let q be a prime power and Fq the finite field with q elements. We examine the existence of
irreducible polynomials with prescribed coefficients over Fq. We focus on a conjecture by …

arxiv:2012.07568v1 [math.HO] 9 Dec 2020 Survey on irreducibility of trinomials Page 1
arxiv:2012.07568v1 [math.HO] 9 Dec 2020 Survey on irreducibility of trinomials Biswajit Koley …

Let q be a prime power and¥ q the finite field with q elements. We examine the existence of
irreducible polynomials with prescribed coefficients over¥ q. We focus on a conjecture by …

In an entry pattern matrix A, all entries are indeterminates and the same indeterminate may
appear in multiple positions. For a field F, an F-completion of A results from assigning a …

In this thesis we describe the work in literature on various aspects of the theory of
polynomials over nite elds. We focus on properties like irreducibility and divisibility. We also …

Finite fields play an important role in the implementation of public-key cryptosystems, and
consequently there is much interest in their efficient implementation. It is well known that the …

This thesis is devoted to the study of certain polynomials over finite fields. There are two
sorts of polynomials that we consider. The first sort involves smooth and powerful …