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In this paper, we introduce the notions of [Formula: see text]-polynomial and [Formula: see text]-minimal value set polynomial where [Formula: see text] is a polynomial over a finite field [Formula:… Click to show full abstract
In this paper, we introduce the notions of [Formula: see text]-polynomial and [Formula: see text]-minimal value set polynomial where [Formula: see text] is a polynomial over a finite field [Formula: see text] and [Formula: see text] is a finite subset of an algebraic closure of [Formula: see text]. We study some properties of these polynomials and we prove that the polynomials used by Garcia, Stichtenoth and Thomas in their work on good recursive tame towers are [Formula: see text]-minimal value set polynomials for [Formula: see text], whose [Formula: see text]-value sets can be explicitly computed in terms of the monomial [Formula: see text].
Journal Title: Journal of Algebra and Its Applications
Year Published: 2021
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