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On circulant self-dual codes over small fields

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Abstract

We construct self-dual codes over small fields \({\mathbb {F}_q}\) with q = 3, 4, 5, 7, 8, 9 of moderate length with long cycles in the automorphism group. With few exceptions, the codes achieve or improve the known lower bounds on the minimum distance of self-dual codes.

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Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme (IAKS), Fakultät für Informatik, Universtität Karlsruhe (TH), Am Fasanengarten 5, 76128, Karlsruhe, Germany

    Markus Grassl

  2. Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Technikerstraße 21a, 6020, Innsbruck, Austria

    Markus Grassl

  3. Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada, V8W 3P6

    T. Aaron Gulliver

Authors
  1. Markus Grassl
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  2. T. Aaron Gulliver
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Correspondence to Markus Grassl.

Additional information

Communicated by V.D. Tonchev.

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Grassl, M., Gulliver, T.A. On circulant self-dual codes over small fields. Des. Codes Cryptogr. 52, 57–81 (2009). https://doi.org/10.1007/s10623-009-9267-1

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  • DOI: https://doi.org/10.1007/s10623-009-9267-1

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