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Zap. Nauchn. Sem. POMI, 2014, Volume 421, Pages 152–165 (Mi znsl5757)  

Classification of permutation fewnomials over simple finite fields

M. A. Rybalkin

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

Abstract: We present a method for permutation trinomials and quadrinomials enumeration based on various symmetries and algebraic properties for search space reduction. Using this method, we enumerated all permutation trinomials and quadrinomials for the prime finite fields with orders up to 3000 and 500 respectively. Based on the enumeration results, we stated a hypothesis about permutation polynomials classification over prime finite fields. We evaluated randomness of such permutations.

Key words and phrases: permutation polynomials classification, permutation binomials, permutation trinomials, permutation quadrinomials.

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English version:
Journal of Mathematical Sciences (New York), 2014, 200:6, 734–741

Document Type: Article
UDC: 512.62
Received: 17.12.2013

Citation: M. A. Rybalkin, “Classification of permutation fewnomials over simple finite fields”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 152–165; J. Math. Sci. (N. Y.), 200:6 (2014), 734–741

Citation in format AMSBIB
\Bibitem{Ryb14}
\by M.~A.~Rybalkin
\paper Classification of permutation fewnomials over simple finite fields
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 421
\pages 152--165
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5757}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 200
\issue 6
\pages 734--741
\crossref{https://doi.org/10.1007/s10958-014-1966-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84940248884}


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