Bent Functions and Permutation Methods

Basic Concepts and Notations.- Gibbs Derivatives on Finite Abelian Groups.- Gibbs Characterization of Binary Bent Functions.- Gibbs Characterisation of Ternary Bent Functions.- Gibbs Characterization of a Class of Quaternary Bent Functions.- Matrix-valued Binary Bent Functions.- Matrix-valued Ternary Bent Functions.- Construction of Bent Functions by FFT-like Permutation Matrices.- Construction of Ternary Bent Functions Trough Matrix Representations.

Radomir S. Stankovic received the B.Sc. degree in electronic engineering from the Faculty of Electronics, University of Nis, Serbia, in 1976, and M.Sc. and Ph.D. degrees in applied mathematics from the Faculty of Electrical Engineering, University of Belgrade, Serbia, in 1984 and 1986, respectively. He was a Professor at the Department of Computer Science, Faculty of Electronics, University of Nis, Serbia, until 2017, when he moved at the Mathematical Institute of SASA, Belgrade, Serbia, working there until 2019, when he is retired. In 1997, he was awarded by the Kyushu Institute of technology Fellowship and worked as a visiting researcher at the Department of Computer Science and Electronics, Kyushu Institute of Technology, Iizuka, Fukuoka, Japan. In 2000 he was awarded by the Nokia Professorship by Nokia, Finland. From 1999 until 2017, he worked in part at the Tampere International Center for Signal Processing, Department of Signal Processing, Faculty of Computing and Electrical Engineering, Tampere University of Technology, Tampere, Finland, first as a visiting professor and from 2009 until 2017 as an adjunct professor. His research interests include switching theory, multiple-valued logic, spectral techniques, and signal processing. He is an author of a few books, three of them, with Jaakko Astola, published by Springer, and another two with Jaakko Astola and Claudio Moraga, published by Wiley/IEEE Press, and Claypool & Morgan.

Milena Stankovic received the B.Sc. degree in electronic engineering from the Faculty of Electronics, University of Nis, Serbia, in 1976, and M. Sc., and Ph. D. degrees in Computing by the same Faculty in 1982 and 1988, respectively. She was a Professor at the Department of Computer Science, Faculty of Electronics, University of Nis, Serbia, until 2018, when she is retired. Milena Stankovic served as the Head of the Department of Computing in 2003 to 2005, and again in 2016 to 2018. Her research interests include switching