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On factorization of some permutation polynomials over finite fields

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Kalaycı, Tekgül (2018) On factorization of some permutation polynomials over finite fields. [Thesis]

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Official URL: http://risc01.sabanciuniv.edu/record=b2057958 (Table of Contents)

Abstract

Factorization of polynomials over finite fields is a classical problem, going back to the 19th century. However, factorization of an important class, namely, of permutation polynomials was not studied previously. In this thesis we present results on factorization of permutation polynomials of Fq,q 2: In order to tackle this problem, we consider permutation polynomials Fn(x)2 Fq[x], n 0; which are defined recursively as compositions of monomials of degree d with gcd(d;q {u100000} 1) = 1, and linear polynomials. Extensions of Fq defined by using the recursive structure of Fn(x) satisfy particular properties that enable us to employ techniques from Galois theory. In consequence, we obtain a variety of results on degrees and number of irreducible factors of the polynomials Fn(x).

Item Type:Thesis
Uncontrolled Keywords:Finite fields. -- Permutation polynomials. -- Factorization of polynomials. -- Irreducible polynomials. -- Sonlu cisimler. -- Permütasyon polinomları. -- Polinomların çarpanlara ayrılması. -- İndirgenemez polinomlar.
Subjects:Q Science > QA Mathematics
ID Code:36860
Deposited By:IC-Cataloging
Deposited On:21 Feb 2019 10:20
Last Modified:25 Mar 2019 17:32

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