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)

Official URL: http://dx.doi.org/10.1016/j.ffa.2019.03.006

## 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 |
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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: | 13 Jun 2023 15:17 |

URI: | https://research.sabanciuniv.edu/id/eprint/38548 |