On the characterization of minimal value set polynomials

2011/08/09 by Herivelto Borges, Borges, Herivelto, Ricardo Conceição +1 · 2 citations
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1108.1852

19 pages

arxiv created 2011/08/09 · arxiv updated 2011/08/10

Abstract

We give an explicit characterization of all minimal value set polynomials in \F_q[x] whose set of values is a subfield \F_q' of \F_q. We show that the set of such polynomials, together with the constants of \F_q', is an \F_q'-vector space of dimension 2^[\F_q:\F_q']. Our approach not only provides the exact number of such polynomials, but also yields a construction of new examples of minimal value set polynomials for some other fixed value sets. In the latter case, we also derive a non-trivial lower bound for the number of such polynomials.

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• Minimal value set binomials and Frobenius nonclassical curves
• Minimal Value Set Polynomials

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