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A note on polynomials with minimal value set over finite fields

Published online by Cambridge University Press:  26 February 2010

Javier Gomez-Calderon
Javier Gomez-Calderon
Affiliation:
Department of Mathematics, New Kensington Campus, The Pennsylvania State University, 3550 Seventh Street Road, New Kensington, PA 15068, U.S.A.
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Abstract

Let f(x) be a polynomial of degree d over Fq, the finite field with q = pn elements. Let V(f) denote the number of distinct values of f(x), xєFq. Then, it is easy to see that

where [x] denotes the greatest integer ≤x. A polynomial for which equality is achieved in (1) is called a minimal value set polynomial. Minimal value set polynomials have been studied in [1] and [3].

Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 144 - 148
Copyright
Copyright © University College London 1988

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References

1.Carlitz, L., Lewis, D. J., Mills, W. H. and Straus, E. G.. Polynomials over finite fields with minimal value set. Mathematika, 8 (1961), 121–130.CrossRefGoogle Scholar
2.Gomez-Calderon, J. and Madden, D. J.. Polynomials with small value sets over finite fields. J. Number theory, 28 (1988), 167–188.CrossRefGoogle Scholar
3.Mills, W. H.. Polynomials with minimal value sets. Pacific J. of Math., 14 (1964), 225–241.CrossRefGoogle Scholar