### 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) |
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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 | |

State | Published - Jan 1 2014 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Applied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday*(pp. 280-296). Cambridge University Press. https://doi.org/10.1017/CCO9781139696456.016

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*Applied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday.*Cambridge University Press, pp. 280-296. https://doi.org/10.1017/CCO9781139696456.016

**Index bounds for value sets of polynomials over finite fields.** / Mullen, Gary Lee; Wan, Daqing; Wang, Qiang.

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

TY - CHAP

T1 - Index bounds for value sets of polynomials over finite fields

AU - Mullen, Gary Lee

AU - Wan, Daqing

AU - Wang, Qiang

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84954202531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84954202531&partnerID=8YFLogxK

U2 - 10.1017/CCO9781139696456.016

DO - 10.1017/CCO9781139696456.016

M3 - Chapter

AN - SCOPUS:84954202531

SN - 9781107074002

SP - 280

EP - 296

BT - Applied Algebra and Number Theory

PB - Cambridge University Press

ER -