Finite Fields and Their Applications 

TL;DR: There are today no sporadic examples of difference sets with Singer parameters; i.e. every known such difference set belongs to a series given by a constructive theorem.

TL;DR: This work surveys the contributions made to permutation polynomials over finite fields in recent years and places emphasis on significant results and novel methods.

TL;DR: In this article, the authors constructed digital (t, s)-sequences in a prime-power base, where the quality parameter was defined as the least possible order of magnitude, using algebraic function fields over the finite field of order, which contained many places of degree 1 relative to the genus.

TL;DR: This paper considers the cross-correlation between a binary m-sequence of length 2m?1 and a decimation of that sequence by an integer t, and presents a method of proving many of these known or conjectured results, including all of the above cases, in a unified way.

TL;DR: This work proposes a unified treatment for a large set of classes of permutation polynomials of F"q and yields a recipe for constructing several new and old classes ofpermutations.