The equivalence of almost bent and almost perfect nonlinear functions and their generalizations [Elektronische Ressource] / von Lilya Budaghyan

THE EQUIVALENCE OF ALMOST BENT ANDALMOST PERFECT NONLINEAR FUNCTIONSAND THEIR GENERALIZATIONSDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)genehmigt durch die Fakult¨at fu¨r Mathematikder Otto-von-Guericke-Universit¨at Magdeburgvon Dipl. Math. Lilya Budaghyangeb. am 29.01.1976 in Baku (Azerbaijan)Gutachter:Prof. Dr. rer. nat. habil. Alexander PottProf. Dr. rer. nat. habil. Tor HellesethProf. Dr. rer. nat. habil. Yuri MovsisyanEingereicht am: 05.10.2005Verteidigung am: 07.12.2005iiDedicationTo my grandparents, Emma and Yakov, my parents, Karina and Mikhail, and my sisterand brother, Milena and Yanik.iiiiv DEDICATIONAcknowledgmentsFirst and formost I thank my family and friends for their constant love, support and en-couragement which enabled this work.I am very grateful to Professor Alexander Pott for having supervised this work while thesame time letting me a huge amount of liberty in my research which I appreciated verymuch. I thank Professor Pott for many mathematical discussions and patience in the firststage of my study, which helped me to get an insight into the field of research in a shorttime. I am very grateful to the opportunity to cooperate with Professor Claude Carletfrom the University of Paris 8. I would like to thank Professor Carlet for the sustainedflow of mathematical inspiration, professional advice and for the invaluable experience Igained from our mutual investigations.