Article

# On the cycle structure of permutation polynomials.

Sabancı University, MDBF, Orhanlı, 34956 Tuzla, İstanbul, Turkey

Finite Fields and Their Applications (Impact Factor: 0.68). 01/2008; 14:593-614. DOI: 10.1016/j.ffa.2007.08.003 Source: DBLP

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**ABSTRACT:**Classes of permutations of finite fields with various specific properties are often needed for applications. We use a recent classification of permutation polynomials using their Carlitz rank with advantage, to produce examples of classes of permutations of F"p, for odd p, which for instance are ''random'', have low differential uniformity, prescribed cycle structure, high polynomial degree, large weight and large dispersion. They are also easy to implement. We indicate applications in coding and cryptography.Journal of Computational and Applied Mathematics 03/2014; 259:536-545. · 0.99 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**L. Carlitz proved that any permutation polynomial f of a finite field FqFq is a composition of linear polynomials and the monomials xq−2xq−2. This result motivated the study of Carlitz rank of f, which is defined in 2009 to be the minimum number of inversions xq−2xq−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.Journal of Symbolic Computation 01/2013; · 0.39 Impact Factor -
##### Conference Paper: Self-inverse interleavers based on permutation functions for turbo codes

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**ABSTRACT:**In this work we introduce and study a set of new interleavers based on permutation functions with known inverses over a finite field F<sub>q</sub> for using in turbo code structures. We use Möbius and Rédei functions in order to find new interleavers. As a byproduct we give an exact formula for finding the inverse of every Rédei function. The cycle structure of Rédei functions are also investigated. Finally, self-inverse versions of permutation functions are used to construct interleavers. These interleavers are their own de-interleavers and are useful for turbo coding and turbo decoding. Experiments carried out for self-inverse interleavers show excellent agreement with our theoretical results.Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on; 11/2010

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