On the characterization of minimal value set polynomials

Author(s)

Borges, Herivelto ^[1] ; Conceicao, Ricardo ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[2] Emory Univ, Oxford Coll, Oxford, GA 30054 - USA

• Document type: Journal article
• Source: JOURNAL OF NUMBER THEORY; v. 133, n. 6, p. 2021-2035, JUN 2013.
• Web of Science Citations: 7

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({[}Fq:Fq']). 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. (C) 2012 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 11/19446-3 - Algebraic curves over finite fields
• Grantee: Herivelto Martins Borges Filho
• Support Opportunities: Regular Research Grants