BENT FUNCTIONS

Bent functions have connections into various areas of mathe matics and computer science which makes them an interesting object to study. This thesis is meant as a comprehensive study summarizing ma y of the results published in the last 40 years. In the first chapter we will motivate the definition of bent fun ctions before we discuss some basic properties in chapter 2. This is done with a sp ecial emphasis on the investigation of restrictions of bent functions to hypersp aces. The obtained results will be used in chapter 3 to deduce conne ctio s of bent functions to various other mathematical structures. Though most resu lts are well-known, we present some new, compressed proofs. Chapter 4 presents four different constructions of bent fun ctio s. Besides the two classical methods proposed by Maiorana/McFarland and Dill on we study two recent constructions by Seberry and Carlet, the latter of which lea ds to some useful general results. The last chapter focuses on the investigation special class es of bent functions. I would like to thank everyone who bore with me during my work o n this thesis. I’m particularly grateful to my family for their support notnly in the last few weeks. They have been backing me up throughout all my time at univers ity. Moreover, I would like to thankfully mention Prof. Dempwolf f for his advise. I enjoyed our discussions we have had over the last years about mathema tical as well as nonmathematical topics a lot.

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