Article

On the cycle structure of permutation polynomials

Sabancı University, MDBF, Orhanlı, 34956 Tuzla, İstanbul, Turkey
Finite Fields and Their Applications (Impact Factor: 0.93). 07/2008; 14(3):593-614. DOI: 10.1016/j.ffa.2007.08.003
Source: DBLP

ABSTRACT

The Silences of the Archives, the Reknown of the Story.
The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, before captivated judges and a guilty feeling Bertrande de Rols. The historian wanted to go beyond the known story in order to discover the world of the heroes. This research led to disappointments and surprizes as documents were discovered concerning the environment of Artigat’s inhabitants and bearing directly on the main characters thanks to notarial contracts. Along the way, study of the works of Coras and Lesueur took a new direction. Coming back to the affair a quarter century later did not result in finding new documents (some are perhaps still buried in Spanish archives), but by going back over her tracks, the historian could only be struck by the silences of the archives that refuse to reveal their secrets and, at the same time, by the possible openings they suggest, by the intuition that almost invisible threads link here and there characters and events.

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Available from: Ayca Cesmelioglu, Aug 03, 2015
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    • "But this is not the case for interleavers derived from permutations like T . The next theorem cited from [3] "

    Full-text · Dataset · Aug 2015
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    • "The cycle structure of Dickson permutation polynomials D n (x, a) where a ∈ {0, ±1} has been studied in [17]. The cycle structure of Möbius transformation has been described in [7]. "
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    ABSTRACT: In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a �nite �eld F_q. For the �rst time Mobius and R�edei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to �nd new interleavers with known cycle structure. In the case of R�edei functions an exact formula for the inverse function is derived. The cycle structure of R�edei functions is also investigated. The self-inverse and non-self-inverse versions of these permutation functions can be used to construct new interleavers.
    Full-text · Article · Jan 2012 · Advances in Mathematics of Communications
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    • "But this is not the case for interleavers derived from permutations like T . The next theorem cited from [4] "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field $\mathbb{F}_q$. For the first time M\"{o}bius and R\'edei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of R\'edei functions an exact formula for the inverse function is derived. The cycle structure of R\'edei functions is also investigated. The self-inverse and non-self-inverse versions of these permutation functions can be used to construct new interleavers.
    Full-text · Article · Nov 2010 · Advances in Mathematics of Communications
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