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

摘要

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. (C) 2020 Elsevier Inc. All rights reserved.