Bent Functions and Permutation Methods

The textbook 'Bent Functions and Permutation Methods' offers a comprehensive presentation of bent functions in binary, ternary, and quaternary systems. It stands out from other works by not only addressing the classical binary bent functions but also highlighting the differences in multivalued cases. The authors provide a detailed explanation of the construction methods based on the application of two special permutation matrices. These matrices are derived from a class of differential operators on finite groups as well as from algorithms of the Fast Fourier Transform. The book demonstrates how additional bent functions can be constructed from given bent functions through targeted manipulations, particularly through permutations. These permutations perform spectrally invariant operations that preserve the property of bentness. The methodological approach and theoretical foundations offer valuable insights for both researchers and students in the field. The clear structure and well-founded presentation of mathematical concepts make the book an important resource in the area of natural and engineering sciences.