Designs, Codes and Cryptography

, Volume 87, Issue 1, pp 173–182 | Cite as

Self-dual codes better than the Gilbert–Varshamov bound

  • Alp BassaEmail author
  • Henning Stichtenoth


We show that every self-orthogonal code over \({\mathbb {F}}_q\) of length n can be extended to a self-dual code, if there exists self-dual codes of length n. Using a family of Galois towers of algebraic function fields we show that over any nonprime field \({\mathbb {F}}_q\), with \(q\ge 64\), except possibly \(q=125\), there are infinite families of self-dual codes, which are asymptotically better than the asymptotic Gilbert–Varshamov bound.


Self-dual codes Algebraic geometry codes Gilbert–Varshamov Bound Tsfasman–Vladut–Zink Bound Towers of function fields Asymptotically good codes Quadratic forms Witt’s Theorem 

Mathematics Subject Classification

14G50 94B27 94B65 15A63 11T71 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and SciencesBoğaziçi UniversityBebekTurkey
  2. 2.Sabancı University, MDBFTuzlaTurkey

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