Investigation of automorphism group for code associated with optimal curve of genus three
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.
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Keywords
automorphism group of curve, AG-code, automorphism group of code, optimal curve, discriminant of finite field, группа афтоморфизмов кривой, группа автоморфизмов кода, АГ-код, оптимальная кривая, дискриминант конечного поляAuthors
| Name | Organization | |
| Malygina E. S. | Kant Baltic Federal University | Ekkat@inbox.ru |
References
Stichtenoth H. Algebraic Function Fields and Codes. Springer, 2009.
Alekseenko E., Aleshnikov S., Markin N., and Zaytsew A. Optimal curves over finite fields with discriminant -19 // Finite Fields and Their Applications. 2011. No. 17(4). P. 350-358.
Milne J. S. Abelian Varieties. 2008. www.jmilne.org/math/
Alekseenko E. and Zaytsew A. Explicit equations of optimal curves of genus 3 over certain fields with three parametrs // Contemporary Math. 2015. No. 637. P. 245-256.
Xing C. Automorphism group of elliptic codes // Communication in Algebra. 1995. No. 23(11). P. 4061-4072.
Xing C. On automorphism groups of the Hermitian codes // IEEE Trans. Inform. Theory. 1995. No. 41(6). P. 1629-1635.
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. 2001. No. 10(1). P. 19-36.
Stichtenoth H. On automorphisms of geometric Goppa codes // J. Algebra. 1990. V. 130. Iss. 1. P. 113-121.
