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Block-transitive algebraic geometry codes attaining the Tsfasman-Vladut-Zink bound

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arxiv 1710.02395 v2 pith:3EOWRCQT submitted 2017-10-05 math.NT math.CO

María Chara , Ricardo A. Podestá , Ricardo Toledano This is my paper · ORCID
classification math.NTmath.CO
keywords codesalgebraicattainingblock-transitiveboundfamilyfieldsgeometry
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We study the asymptotic behavior of a family of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. We prove, by using towers of algebraic function fields, that there are sequences of codes in this family attaining the Tsfasman-Vladut-Zink bound over finite fields of square cardinality. We give the exact length of these codes as well as explicit lower bounds for their parameters.

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