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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 10 scientific papers (total in 10 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 (10)
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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known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area.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
Russian version:
Uspekhi Matematicheskikh Nauk, 2021, Volume 76, Issue 1(457), Pages 31–94
DOI: https://doi.org/10.4213/rm9928
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”, Uspekhi Mat. Nauk, 76:1(457) (2021), 31–94; Russian Math. Surveys, 76:1 (2021), 29–89
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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