A construction of bent functions from plateaued functions
From the introduction: We present a technique for constructing bent functions from plateaued functions which generalizes earlier constructions of bent functions from near-bent functions. Though the technique also works for \(p=2\), we assume in the following that \(p\) is odd, as we are mainly interested in this type of functions, which we will also call \(p\)-ary functions. In Sect. 2 we analyze the Fourier spectrum of quadratic functions and the effect of equivalence transformations to the Fourier spectrum. In particular, we show under which conditions the product of a \(p\)-ary function with a constant changes the signs in the Fourier spectrum. The procedure for constructing bent functions from \(s\)-plateaued functions is presented in Sect. 3. In Sect. 4 we point out that the construction delivers a large variety of provable inequivalent bent functions, and we give some simple examples of weakly regular and non-weakly regular bent functions. Bent functions with some additional properties can be used to construct strongly regular graphs. We will show how to obtain a large variety of such bent functions. Finally, we present simple explicit expressions for bent function in odd dimension with maximal possible degree.
scientific article; zbMATH DE number 6131790
scientific article