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The Carlitz rank of permutations of finite fields: a survey

Topuzoğlu, Alev (2014) The Carlitz rank of permutations of finite fields: a survey. Journal of Symbolic Computation (SI), 64 . pp. 53-66. ISSN 0747-7171

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Official URL: http://dx.doi.org/10.1016/j.jsc.2013.07.004

Abstract

L. Carlitz proved that any permutation polynomial f of a finite field Fq is a composition of linear polynomials and the monomials xq−2. This result motivated the study of Carlitz rank of f, which is defined in 2009 to be the minimum number of inversions xq−2, needed to obtain f, by E. Aksoy et al. We give a survey of results obtained so far on natural questions related to this concept and indicate a variety of applications, which emerged recently.

Item Type:Article
Uncontrolled Keywords:Permutation polynomials over finite fields; Carlitz rank; Dispersion; Pseudorandom number generators; Generalized van der Corput sequences
Subjects:Q Science > QA Mathematics > QA150-272.5 Algebra
ID Code:23158
Deposited By:Alev Topuzoğlu
Deposited On:17 Jan 2014 15:11
Last Modified:15 Nov 2014 20:31

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