Geodesic
On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 1, pp. 29-89

Voir la notice de l'article provenant de la source Math-Net.Ru

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known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area.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. 
@article{RM_2021_76_1_a1,
     author = {S. Ballet and J. Pieltant and M. Rambaud and H. Randriambololona and R. Rolland and J. Chaumine},
     title = {On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {29--89},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2021_76_1_a1/}
}
TY  - JOUR
AU  - S. Ballet
AU  - J. Pieltant
AU  - M. Rambaud
AU  - H. Randriambololona
AU  - R. Rolland
AU  - J. Chaumine
TI  - On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2021
SP  - 29
EP  - 89
VL  - 76
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2021_76_1_a1/
LA  - en
ID  - RM_2021_76_1_a1
ER  - 
%0 Journal Article
%A S. Ballet
%A J. Pieltant
%A M. Rambaud
%A H. Randriambololona
%A R. Rolland
%A J. Chaumine
%T On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 29-89
%V 76
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2021_76_1_a1/
%G en
%F RM_2021_76_1_a1
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. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 1, pp. 29-89. http://geodesic.mathdoc.fr/item/RM_2021_76_1_a1/