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 | |
| State | Published - Jan 1 2014 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 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 -