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

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Abstract

Let Vf denote the value set (image) of a polynomial f ε Fq[x]. We relate the number of polynomials f ∈ Fq[x] of degree q - 1 such that Vf = k to the solutions (xl,...,xk) of a linear equation over Fq, with the added restriction that xi≠xj whenever i≠j. Using this we find a simple formula for the number of such polynomials.

Original languageEnglish (US)
Pages (from-to)168-174
Number of pages7
JournalFinite Fields and their Applications
Volume9
Issue number2
DOIs
StatePublished - Apr 1 2003

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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