Near bent functions on a hyperplane
type: Item
instance of: scholarly article
title: Near bent functions on a hyperplane
zbMATH Open document ID: 1159.11051
author: Gary McGuire
author: J. F. Dillon
published in: Finite Fields and their Applications
publication date: 2008-08-27T00:00:00Z
review text: The authors show that the Kasami-Welch near bent function \(f(x) = \text{Tr}(x^{4^k-2^k+1})\) from \(\mathbb F_{2^n}\) to \(\mathbb F_2\) (\(n\) odd) restricted to the hyperplane \(H = \{x \in \mathbb F_{2^n}\mid\text{Tr}(x) = 0\}\) of \(\mathbb F_{2^n}\) is bent for \(n = 3k \pm 1\). Moreover \(f(x) = \text{Tr}(x^{4^k-2^k+1})\) is not bent when restricted to any other hyperplane. In order to prove this result a criterion for near bent functions to be bent on hyperplanes is given. With this criterion the authors also reprove a similar result on bent restrictions to a hyperplane of Gold functions first shown in \textit{J. Lahtonen, G. McGuire} and \textit{H. N. Ward} [Adv. Math. Commun. 1, 243--250 (2007)].
reviewed by: Wilfried Meidl
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 12E20
zbMATH DE Number: 5316923
zbMATH Keywords: Bent function
zbMATH Keywords: Kasami-Welch near bent function
zbMATH Keywords: hyperplane
zbMATH Keywords: finite field
zbMATH Keywords: Fourier spectrum
MaRDI profile type: Publication
full work available at URL: j.ffa.2007.11.001
OpenAlex ID: W1992704551
cites work: On cryptographic properties of the cosets of R(1, m)
cites work: Q4365754
cites work: Multiplicative difference sets via additive characters
cites work: Another proof of Kasami's theorem
cites work: Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)
cites work: The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes
cites work: Analysis of Kasami-Welch functions in odd dimension using Stickelberger's theorem
cites work: Gold and Kasami-Welch functions, quadratic forms, and bent functions
DOI: 10.1016/J.FFA.2007.11.001
description: scientific article; zbMATH DE number 5316923