Geodesic
Investigation of automorphism group for code associated with optimal curve of genus three
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 115-117.

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

Here, we have proved that under certain conditions, the automorphism group of optimal curve of genus three over finite field with discriminant from $\{-19,-43,-67,-163\}$ is isomorphic to the automorphism group of AG-code associated with such a curve.
Keywords: optimal curve, discriminant of finite field, automorphism group of curve.
Mots-clés : AG-code, automorphism group of code 
@article{PDMA_2018_11_a35,
     author = {E. S. Malygina},
     title = {Investigation of automorphism group for code associated with optimal curve of genus three},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {115--117},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2018_11_a35/}
}
TY  - JOUR
AU  - E. S. Malygina
TI  - Investigation of automorphism group for code associated with optimal curve of genus three
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2018
SP  - 115
EP  - 117
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2018_11_a35/
LA  - ru
ID  - PDMA_2018_11_a35
ER  - 
%0 Journal Article
%A E. S. Malygina
%T Investigation of automorphism group for code associated with optimal curve of genus three
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2018
%P 115-117
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2018_11_a35/
%G ru
%F PDMA_2018_11_a35
E. S. Malygina. Investigation of automorphism group for code associated with optimal curve of genus three. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 115-117. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a35/

[1] Stichtenoth H., “On automorphisms of geometric Goppa codes”, J. Algebra, 130:1 (1990), 113–121 | DOI | MR | Zbl

[2] Xing C., “Automorphism group of elliptic codes”, Communication in Algebra, 23:11 (1995), 4061–4072 | DOI | MR | Zbl

[3] Xing C., “On automorphism groups of the Hermitian codes”, IEEE Trans. Inform. Theory, 41:6 (1995), 1629–1635 | DOI | MR | Zbl

[4] Lauter K., “Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields. With an appendix by J.-P. Serre”, Algebraic Geometry, 10:1 (2001), 19–36 | MR | Zbl

[5] Milne J. S., Abelian Varieties, , 2008 http://www.jmilne.org/math/

[6] Alekseenko E., Zaytsew A., “Explicit equations of optimal curves of genus 3 over certain fields with three parametrs”, Contemporary Math., 637 (2015), 245–256 | DOI | MR

[7] Alekseenko E., Aleshnikov S., Markin N., Zaytsew A., “Optimal curves over finite fields with discriminant $-19$”, Finite Fields and Their Applications, 17:4 (2011), 350–358 | DOI | MR | Zbl

[8] Stichtenoth H., Algebraic Function Fields and Codes, Springer, 2009 | MR | Zbl