On components of vectorial permutations of F-q(n)

Anbar Meidl, Nurdagül and Kaşıkcı, Canan and Topuzoğlu, Alev (2019) On components of vectorial permutations of F-q(n). Finite Fields and Their Applications, 58 . pp. 124-132. ISSN 1071-5797 (Print) 1090-2465 (Online)

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Abstract

We consider vectorial maps F(x(1), ..., x(n)) = (f(1) (x(1), ..., x(n)), ..., f(n) (x(1), ..., x(n))) : F-q(n) bar right arrow F-q(n), which induce permutations of F-q(n) . We show that the degrees of the components f(1), f(2), ..., f(n) is an element of F-q [x(1), ..., x(n)] are at least 2 when 2 <= deg(F) = d < root q and d vertical bar (q - 1) Our proof uses an absolutely irreducible curve over F-q and the number of rational points on it that we relate to the cardinality of the value set of a polynomial.
Item Type: Article
Uncontrolled Keywords: Curves over finite fields; Local permutation polynomials; Vectorial permutations
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Alev Topuzoğlu
Date Deposited: 25 Aug 2019 19:35
Last Modified: 26 Apr 2022 10:10
URI: https://research.sabanciuniv.edu/id/eprint/38548

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