Preface to the special issue on ArasuFest

Abstract

On the occasion of K.T. Arasu's 65th birthday, a conference "Sequences, Codes and Designs" took place at Kalamata (Greece), August 1-4, 2019. More than 30 talks covered Arasu's research interest in many different areas of discrete mathematics. The contributions in this volume are partially based on these talks, but one may also find papers from researchers who could not attend the conference.The articles in this volume focus on topics in sequences, codes and designs, related to K.T. Arasu's influential work. All submissions have been thoroughly reviewed by at least two referees.Arasu wrote his PhD thesis under the supervision of D.K. Ray-Chaudhuri about difference lists. Difference lists occur as homomorphic images of (putative) difference sets. The goal is to rule out the existence of such difference lists in order to rule out the existence of difference sets. In his thesis, Arasu developed a theory of such difference lists, and later on, he was able to rule out the existence of several difference sets whose existence has been undecided in the famous "Lander's tables" [12]. Let us mention [1,2,9] as some examples from this early scientific career of K.T. Arasu.Since 1990, Arasu became interested in divisible and, as a special subcase, relative difference sets. It turned out that such divisible difference sets are closely related to projective planes admitting quasiregular automorphism groups, in particular semifields, as well as (vectorial) bent functions. Both these topics still attract many researchers! A paper that appeared in that period is the solution of the Waterloo problem [4], which deals with possible extensions of difference sets to relative difference sets.