Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

Institution:	1. Institut de Mathématiques de Toulon - IMATH, Université de Toulon, France;2. Institut de Mathématiques de Marseille - I2M, Aix-Marseille Université, UMR 7373 CNRS, Centrale Marseille, France;3. INSPE Nice-Toulon, Université Côte d''Azur, France;4. Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UT2J, F-31058 Toulouse, France;1. Department of Ophthalmology, Zekai Tahir Burak Women''s Health Research and Education Hospital, Ankara, Turkey;2. Department of Ophthalmology, Hacettepe University, Faculty of Medicine, Ankara, Turkey;3. Department of Biostatistics, Hacettepe University, Faculty of Medicine;1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet 303B, 2800 Kgs. Lyngby, Denmark;2. Department of Mathematics and Statistics, University of Tromsø, Hansine Hansens veg 18, 9019, Norway;1. Departamento de Matemáticas, Universidad de León, Spain;2. Departamento de Matemáticas, Universidad de Salamanca, Spain

Abstract:	We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption that the abelian surface does not contain low genus curves. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization.

Keywords:	Abelian surfaces AG codes Weil restrictions Finite fields
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