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Self-dual codes better than the Gilbert–Varshamov bound

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Boğaziçi University, 34342, Bebek, İstanbul, Turkey

    Alp Bassa

  2. Sabancı University, MDBF, 34956, Tuzla, İstanbul, Turkey

    Henning Stichtenoth

Authors
  1. Alp Bassa
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  2. Henning Stichtenoth
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Corresponding author

Correspondence to Alp Bassa.

Additional information

Communicated by J. Bierbrauer.

A.B. was supported by the BAGEP Award of the Science Academy with funding supplied by Mehveş Demiren in memory of Selim Demiren and TÜBİTAK Proj. 112T233. H.S. was supported by TÜBİTAK Proj. 114F432.

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Bassa, A., Stichtenoth, H. Self-dual codes better than the Gilbert–Varshamov bound. Des. Codes Cryptogr. 87, 173–182 (2019). https://doi.org/10.1007/s10623-018-0497-y

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  • DOI: https://doi.org/10.1007/s10623-018-0497-y

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