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 …

We consider the problem of enumerating irreducible transformation shift registers. We give
an asymptotic formula for the number of irreducible transformation shift registers in some …

A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree
over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula …

We consider the problem of counting the number of linear transformation shift registers
(TSRs) of a given order over a finite field. We derive explicit formulae for the number of …

Abstract Let R (x)= g (x)/h (x) be a rational expression of degree three over the finite field F q.
We count the irreducible polynomials in F q [x], of a given degree, that have the form h (x) …

We study and partially classify cubic rational expressions $ g (x)/h (x) $ over a finite field
$\mathbb {F} _q $, up to pre-and post-composition with independent M\" obius …

In this thesis we consider some problems concerning polynomials over finite fields. The first
topic is the action of some groups on irreducible polynomials. We describe orbits and …

For any finite field $\mathbb {F} $ and any positive integer $ n $ we count the number of
monic polynomials of degree $ n $ over $\mathbb {F} $ with nonzero constant coefficient and …

Let f (x) be an irreducible polynomial of degree m over the finite field Fq where q is a power
of 2. We show that the polynomial x2mf (x 4+ x3+ x+ 1 x2) is an irreducible polynomial of …

Lenstra, in this Monthly, has pointed out that a cubic over F 5= Z/5 Z of the form (x− a)(x−
b)(x− c)+ λ (x− d)(x− e), where {a, b, c, d, e} is some permutation of {0, 1, 2, 3, 4}, is …