Permutations of finite fields for check digit systems
type: Item
instance of: scholarly article
title: Permutations of finite fields for check digit systems
zbMATH Open document ID: 1248.11100
author: Rasha Shaheen
author: Arne Winterhof
published in: Designs, Codes and Cryptography
publication date: 2010-10-13T00:00:00Z
review text: From the authors' abstract: Let \(q\) be a prime power and \(n\) a positive divisor of \(q-1\). We prove an asymptotic formula for the number of polynomials \[ f(X)=\frac{a-b}{n}\bigg(\sum_{j=1}^{n-1} X^{j(q-1)/n}\bigg)X+\frac{a+b(n-1)}{n}\,X\in\mathbb{F}_q[X] \] such that the polynomials \(f(X)\), \(f(X)\pm X\), and \(f(f(X))\pm X\) are all permutation polynomials over \(\mathbb{F}_q\).
reviewed by: Astrid Reifegerste
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11T22
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 5799402
zbMATH Keywords: check digit systems
zbMATH Keywords: finite fields
zbMATH Keywords: permutation polynomials
zbMATH Keywords: orthomorphisms
zbMATH Keywords: complete mappings
zbMATH Keywords: cyclotomy
MaRDI profile type: Publication
full work available at URL: s10623-010-9374-z
OpenAlex ID: W2141445884
cites work: Q4807506
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DOI: 10.1007/S10623-010-9374-Z
description: scientific article; zbMATH DE number 5799402