Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find




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

Russian Mathematical Surveys, 2021, Volume 76, Issue 1, Pages 29–89
DOI: https://doi.org/10.1070/RM9928 (Mi rm9928) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry

S. Balleta, J. Pieltantb, M. Rambaudc, H. Randriambololonad, R. Rollanda, J. Chauminee

a Aix-Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, Marseille, France
b Équipe en émergence Sécurité-Défense, Conservatoire National des Arts et Métiers, Paris, France
c LTCI, Télécom ParisTech, Institut Polytechnique de Paris, Paris, France
d Laboratoire de Cryptographie, Agence Nationale de Sécurité des Systèmes d'Information, Paris, France
e Laboratoire Géométrie Algébrique et Applications à la Théorie de l'Information, Université de la Polynésie Française, Tahiti, France
English version PDF (984 kB) Citations (11) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/RM9928
Abstract: In this paper, we give a survey of the known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area. In particular, we identify and clarify certain partially proved results and emphasise links with open problems in number theory, algebraic geometry, and coding theory.
Bibliography: 92 titles.
Keywords: finite field, tensor rank of multiplication, function field.
Received: 17.09.2019
Bibliographic databases:
Document Type: Article
UDC: 512.624+512.75+519.712
MSC: Primary 14H05; Secondary 12E20
Language: English
Original paper language: Russian
Citation: S. Ballet, J. Pieltant, M. Rambaud, H. Randriambololona, R. Rolland, J. Chaumine, “On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry”, Russian Math. Surveys, 76:1 (2021), 29–89
Citation in format AMSBIB
\Bibitem{BalPieRam21}
\by S.~Ballet, J.~Pieltant, M.~Rambaud, H.~Randriambololona, R.~Rolland, J.~Chaumine
\paper On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
\jour Russian Math. Surveys
\yr 2021
\vol 76
\issue 1
\pages 29--89
\mathnet{http://mi.mathnet.ru//eng/rm9928}
\crossref{https://doi.org/10.1070/RM9928}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4223937}
\zmath{https://zbmath.org/?q=an:1482.11164}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021RuMaS..76...29B}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000701542600001}
\elib{https://elibrary.ru/item.asp?id=46815816}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85106963303}
Linking options:
  • https://www.mathnet.ru/eng/rm9928
  • https://doi.org/10.1070/RM9928
  • https://www.mathnet.ru/eng/rm/v76/i1/p31
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:389
    Russian version PDF:128
    English version PDF:46
    Russian version HTML:150
    References:47
    First page:19
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024