RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (223 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.2

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
\Bibitem{IvcMed08} \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 \mathnet{http://mi.mathnet.ru/dm985} \crossref{https://doi.org/10.4213/dm985} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2420493} \zmath{https://zbmath.org/?q=an:05618962} \elib{http://elibrary.ru/item.asp?id=20730225} \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}