Index bounds for value sets of polynomials over finite fields

Gary L. Mullen; Daqing Wan; Qiang Wang

doi:10.1017/CCO9781139696456.016

Index bounds for value sets of polynomials over finite fields

Gary L. Mullen, Daqing Wan, Qiang Wang

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

5 Scopus citations

Abstract

We provide an upper bound for the cardinality of the value set of a univariate polynomial over a finite field in terms of the index of the polynomial. Moreover, we study when a polynomial vector map in n variables is a permutation polynomial map, again using the index tuple of the map. This also provides an upper bound for the value set of a polynomial map in n variables.

Original language	English (US)
Title of host publication	Applied Algebra and Number Theory
Subtitle of host publication	Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday
Publisher	Cambridge University Press
Pages	280-296
Number of pages	17
ISBN (Electronic)	9781139696456
ISBN (Print)	9781107074002
DOIs	https://doi.org/10.1017/CCO9781139696456.016
State	Published - Jan 1 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/CCO9781139696456.016

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AB - We provide an upper bound for the cardinality of the value set of a univariate polynomial over a finite field in terms of the index of the polynomial. Moreover, we study when a polynomial vector map in n variables is a permutation polynomial map, again using the index tuple of the map. This also provides an upper bound for the value set of a polynomial map in n variables.

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BT - Applied Algebra and Number Theory

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ER -

Index bounds for value sets of polynomials over finite fields

Abstract

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