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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 152–165 (Mi znsl5757)  
This article is cited in 1 scientific paper (total in 1 paper)

Classification of permutation fewnomials over simple finite fields

M. A. Rybalkin

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
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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.
Received: 17.12.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 200, Issue 6, Pages 734–741
DOI: https://doi.org/10.1007/s10958-014-1966-0
Bibliographic databases:
Document Type: Article
UDC: 512.62
Language: Russian
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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84940248884}
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  • https://www.mathnet.ru/eng/znsl/v421/p152
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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