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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the characterization of minimal value set polynomials

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Author(s):
Borges, Herivelto [1] ; Conceicao, Ricardo [2]
Total Authors: 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
Total Affiliations: 2
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