Diskretnaya Matematika
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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Diskr. Mat., 2018, Volume 30, Issue 2, Pages 62–72 (Mi dm1507)  

Formulas for a characteristic of spheres and balls in binary high-dimensional spaces

V. G. Mikhailov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider a special function $\rho(H)$ of the subset $H$ of $n$-dimensional vector linear space over the field $K$. This function is used in the estimates of accuracy of the Poisson approximation for the distribution of the number of solutions of systems of random equations and random inclusions over $K$. For the case when $K=GF(2)$ and $H$ is a sphere or ball (in the Hamming metric) in $\{0,1\}^n$ we obtain explicit and approximate formulas for $\rho(H)$ for sufficiently large values of $n$.

Keywords: linear spaces over finite fields, Hamming metric, random linear inclusions.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01


DOI: https://doi.org/10.4213/dm1507

Full text: PDF file (438 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2019, 29:5, 311–319

Bibliographic databases:

UDC: 519.212.2
Received: 13.02.2018

Citation: V. G. Mikhailov, “Formulas for a characteristic of spheres and balls in binary high-dimensional spaces”, Diskr. Mat., 30:2 (2018), 62–72; Discrete Math. Appl., 29:5 (2019), 311–319

Citation in format AMSBIB
\Bibitem{Mik18}
\by V.~G.~Mikhailov
\paper Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
\jour Diskr. Mat.
\yr 2018
\vol 30
\issue 2
\pages 62--72
\mathnet{http://mi.mathnet.ru/dm1507}
\crossref{https://doi.org/10.4213/dm1507}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3849593}
\elib{https://elibrary.ru/item.asp?id=34940590}
\transl
\jour Discrete Math. Appl.
\yr 2019
\vol 29
\issue 5
\pages 311--319
\crossref{https://doi.org/10.1515/dma-2019-0029}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000491422800005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074542074}


Linking options:
  • http://mi.mathnet.ru/eng/dm1507
  • https://doi.org/10.4213/dm1507
  • http://mi.mathnet.ru/eng/dm/v30/i2/p62

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Дискретная математика
    Number of views:
    This page:220
    Full text:5
    References:13
    First page:18

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021