Large set complete mappings over finite fields

Abstract

"This thesis explores set complete mappings and permutation polynomials of a newly defined type. We begin with some preliminaries in Chapter 1 to build up the tools and vocabulary necessary for such an exploration. Then, in Chapter 2, we introduce a new methodology for establishing permutation polynomials from Dembowski-Ostrom polynomials over Fq. In Chapters 3 and 4, we present new classes of permutation polynomials and set complete mappings. In Chapter 5, we survey what is known of monomial set complete mappings and present some computational data. Finally, in Chapter 6, we share a couple of conjectures and plot the course for future work."--Page vii (first paragraph of Preface)