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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Algebra and Number Theory
- Applied Mathematics