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Diskr. Mat., 2008, Volume 20, Issue 1, Pages 3–24 (Mi dm985)  

Random polynomials over a finite field

G. I. Ivchenko, Yu. I. Medvedev


Abstract: We consider monic (with higher coefficient 1) polynomials of fixed degree $n$ over an arbitrary finite field $GF(q)$, where $q\ge2$ is a prime number or a power of a prime number. It is assumed that on the set $\mathscr F_n=\{f_n\}$ of all $q^n$ such polynomials the uniform measure is defined which assigns the probability $q^{-n}$ to each polynomial. For an arbitrary polynomial $f_n\in\mathscr F_n$, its local structure $\mathscr K_n=\mathscr K(f_n)$ is defined as the set of multiplicities of all irreducible factors in the canonical decomposition of $f_n$, and various structural characteristics of a polynomial (its exact and asymptotic as $n\to\infty$ distributions) which are functionals of $\mathscr K_n$ are studied. Directions of possible further research are suggested.

DOI: https://doi.org/10.4213/dm985

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English version:
Discrete Mathematics and Applications, 2008, 18:1, 1–23

Bibliographic databases:

UDC: 519.2
Received: 22.02.2007

Citation: G. I. Ivchenko, Yu. I. Medvedev, “Random polynomials over a finite field”, Diskr. Mat., 20:1 (2008), 3–24; Discrete Math. Appl., 18:1 (2008), 1–23

Citation in format AMSBIB
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\by G.~I.~Ivchenko, Yu.~I.~Medvedev
\paper Random polynomials over a~finite field
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 1
\pages 3--24
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\crossref{https://doi.org/10.4213/dm985}
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\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 1
\pages 1--23
\crossref{https://doi.org/10.1515/DMA.2008.001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-64549144542}


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  • Дискретная математика
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