The only crooked power functions are \(x^{2^k+2^l}\)
type: Item
instance of: scholarly article
title: The only crooked power functions are \(x^{2^k+2^l}\)
zbMATH Open document ID: 1180.94055
author: Gohar M. Kyureghyan
published in: European Journal of Combinatorics
publication date: 2007-04-10T00:00:00Z
review text: A map \(f\colon\mathbb F_ {2^ {n}}\rightarrow\mathbb F_ {2^ n}\) is called crooked if the set \(\{f(x+a)+f(x)\mid x\in\mathbb F_ {2^ {n}}\}\) is the complement of a hyperplane for every fixed \(a\in\mathbb F^ *_ {2^ n}\) (where \(\mathbb F_ {2^ {n}}\) is considered as a vector space over \(\mathbb F_ {2}\)). In Theorem 1 the author proves that the only crooked power maps are the quadratic maps \(x^{2^k+2^l}\) with \(\gcd(n,k-l)=1\). In Theorem 3 a geometrical characterization of crooked maps for almost bent permutations is given, and some connections with almost perfect nonlinear maps are revealed.
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 5141679
reviewed by: Olaf Ninnemann
MaRDI profile type: Publication
full work available at URL: j.ejc.2006.01.010
OpenAlex ID: W2065797172
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DOI: 10.1016/J.EJC.2006.01.010
description: scientific article; zbMATH DE number 5141679