Characterisation and enumeration of a class of semi-bent quadratic Boolean functions
type: Item
instance of: scholarly article
title: Characterisation and enumeration of a class of semi-bent quadratic Boolean functions
zbMATH Open document ID: 1338.94118
DOI: 10.1504/IJICOT.2015.068696
author: Neşe Koçak
author: Onur Koçak
author: Ferruh Özbudak
author: Zülfükar Saygı
published in: International Journal of Information and Coding Theory
publication date: 2016-01-29T00:00:00Z
review text: Summary: In this paper, we consider semi-bentness of quadratic Boolean functions defined for even \(n\) and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for \(6|n\). Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous partial and incomplete enumeration results for three other classes of semi-bent/bent functions in the literature using this method. We also correct some results on quadratic bent functions stated in [\textit{W. Ma} et al., IEICE Trans. Fundam. E-88-A, No. 7, 2039--2040 (2005)].
Mathematics Subject Classification ID: 94C10
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 6537524
zbMATH Keywords: quadratic Boolean functions
zbMATH Keywords: semi-bent functions
zbMATH Keywords: self-reciprocal polynomials
zbMATH Keywords: enumeration
zbMATH Keywords: bent functions
MaRDI profile type: Publication
full work available at URL: ijicot.2015.068696
OpenAlex ID: W2054191520
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description: scientific article; zbMATH DE number 6537524