Index bounds for value sets of polynomials over finite fields

Gary Lee Mullen, Daqing Wan, Qiang Wang

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationApplied Algebra and Number Theory
Subtitle of host publicationEssays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday
PublisherCambridge University Press
Pages280-296
Number of pages17
ISBN (Electronic)9781139696456
ISBN (Print)9781107074002
DOIs
StatePublished - Jan 1 2014

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Galois field
Polynomial Maps
Polynomial
Upper bound
Permutation Polynomial
Univariate
Cardinality

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Mullen, G. L., Wan, D., & Wang, Q. (2014). Index bounds for value sets of polynomials over finite fields. In 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
Mullen, Gary Lee ; Wan, Daqing ; Wang, Qiang. / Index bounds for value sets of polynomials over finite fields. Applied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday. Cambridge University Press, 2014. pp. 280-296
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Mullen, GL, Wan, D & Wang, Q 2014, Index bounds for value sets of polynomials over finite fields. in 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.

Applied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday. Cambridge University Press, 2014. p. 280-296.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Mullen GL, Wan D, Wang Q. Index bounds for value sets of polynomials over finite fields. In Applied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday. Cambridge University Press. 2014. p. 280-296 https://doi.org/10.1017/CCO9781139696456.016