The number of polynomials of a given degree over a finite field with value sets of a given cardinality

Authors:
Pinaki Das
Affiliations:
Department of Mathematics and Statistics, Penn State Altoona, Altoona, PA 16601, USA
Venue:
Finite Fields and Their Applications
Year:
2003

Citing 3
Cited 1

Finite fields

Finite fields
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Value sets of polynomials and the Cauchy Davenport theorem

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Abstract

Let V"f denote the value set (image) of a polynomial f@?F"q[x]. We relate the number of polynomials f@?F"q[x] of degree q-1 such that |V"f|=k to the solutions (x"1,...,x"k) of a linear equation over F"q, with the added restriction that x"ix"j whenever ij. Using this we find a simple formula for the number of such polynomials.