Polynomials with small value set over finite fields
type: Item
instance of: scholarly article
title: Polynomials with small value set over finite fields
zbMATH Open document ID: 0634.12014
DOI: 10.1016/0022-314X(88)90064-9
author: Javier Gomez-Calderon
author: Daniel J. Madden
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Let \(K_ q\) denote the finite field with \(q=p^ r\) elements. Let f(x) be a monic polynomial of degree \(d\) with coefficients in \(K_ q\). Let C(f) denote the number of distinct values of f(x) as x ranges over \(K_ q\). The authors give a complete list of polynomials such that \(d<q^{1/4}\), \(GCD(q,d)=1\) and \(C(f)<2q/d\). The result is obtained [following the work of the reviewer, Can. Math. Bull. 10, 585-594 (1967; Zbl 0185.103)] by using the connection between the size of C(f) and the factorization of f(x)-f(y) in the ring \(K_ q[x,y]\).
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 4031827
zbMATH Keywords: value sets of polynomials in a finite field
reviewed by: Kenneth S. Williams
MaRDI profile type: Publication
cites work: Polynomials over finite fields with minimal value sets
cites work: Q3216750
cites work: Polynomials with minimal value sets
cites work: A Congruence Problem of E. G. Straus
cites work: On Extremal Polynomials
cites work: Note on Dickson's permutation polynomials
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description: scientific article; zbMATH DE number 4031827