TY - JOUR
T1 - On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
AU - Ballet, St'ephane
AU - Pieltant, Julia
AU - Rambaud, Matthieu
AU - Randriambololona, Hugues
AU - Rolland, Robert
AU - Chaumine, Jean
N1 - Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.
PY - 2021/2/1
Y1 - 2021/2/1
N2 - 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known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area.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.
AB - 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known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area.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.
KW - Finite field
KW - Function field
KW - Tensor rank of multiplication
U2 - 10.1070/RM9928
DO - 10.1070/RM9928
M3 - Article
AN - SCOPUS:85106963303
SN - 0036-0279
VL - 76
SP - 29
EP - 89
JO - Russian Mathematical Surveys
JF - Russian Mathematical Surveys
IS - 1
ER -