A construction of bent functions from plateaued functions
type: Item
instance of: scholarly article
title: A construction of bent functions from plateaued functions
zbMATH Open document ID: 1286.06021
author: Wilfried Meidl
author: Ayça Çeşmelioğlu
published in: Designs, Codes and Cryptography
publication date: 2013-01-28T00:00:00Z
full work available at URL: 88.pdf
review text: 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.
Mathematics Subject Classification ID: 06E30
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 6131790
zbMATH Keywords: bent functions
zbMATH Keywords: plateaued functions
zbMATH Keywords: Fourier transform
zbMATH Keywords: strongly regular graphs
zbMATH Keywords: maximal degree
reviewed by: Sergiu Rudeanu
MaRDI profile type: Publication
OpenAlex ID: W2077153543
cites work: Normal Extensions of Bent Functions
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DOI: 10.1007/S10623-012-9686-2
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description: scientific article; zbMATH DE number 6131790