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 …

Elements of high order in finite fields of the form Fq[x]/Φr(x) Page 1 Finite Fields and Their
Applications 18 (2012) 700–710 Contents lists available at SciVerse ScienceDirect Finite Fields …

Elements of high order in Artin–Schreier extensions of finite fields Fq - ScienceDirect Skip to
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Every finite field has many multiplicative generators. However, finding one in polynomial
time is an important open problem. In fact, even finding elements of high order has not been …

We discuss the problem of constructing elements of multiplicative high order in finite fields of
large degree over their prime field. We prove that for points on a plane curve, one of the …

Optimal normal bases are special cases of the so-called Gauss periods (Disquisitiones
Arithmeticae, Articles 343–366); in particular, optimal normal bases are Gauss periods of …

Let V be a fixed algebraic variety defined by m polynomials in n variables with integer
coefficients. We show that there exists a constant C (V) such that for almost all primes p for …

We describe a deterministic algorithm for finding a generator of the multiplicative group of
the finite field with pn elements. In time polynomial in p and n, the algorithm either outputs an …

SHARPENING OF THE EXPLICIT LOWER BOUNDS ON THE ORDER OF ELEMENTS IN
FINITE FIELD EXTENSIONS BASED ON CYCLOTOMIC POLYNOMIALS ПІ Page 1 © R …

On elements of high order in general finite fields Page 1 Algebra and Discrete Mathematics
RESEARCH ARTICLE Volume 18 (2014). Number 2, pp. 295–300 © Journal “Algebra and …