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Constructions of Optimal Linear Codes

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Numbers, Information and Complexity

Abstract

The goal of this paper is to present an overview on known constructions of length-optimal linear codes. First we discuss the interrelation between various definitions of optimality in terms of the basic parameters of a linear code: length, dimension and minimum distance.. Then we give some general constructions of Griesmer codes based on the anticode technique. Constructions using the correspondences between codes and projective multisets are also considered. A survey on quasi-cyclic and quasi-twisted optimal codes is included.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8. G. Bonchev Str, 1113, Sofia, Bulgaria

    Stefan Dodunekov

  2. Faculty of Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, the Netherlands

    Juriaan Simonis

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  1. Stefan Dodunekov
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  2. Juriaan Simonis
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Editor information

Editors and Affiliations

  1. Friedrich Schiller-Universität Jena, Germany

    Ingo Althöfer

  2. National University of Singapore, Singapore

    Ning Cai

  3. IBM Germany, Germany

    Gunter Dueck

  4. Universität Bielefeld, Germany

    Levon Khachatrian

  5. Russian Academy of Sciences, Russia

    Mark S. Pinsker

  6. Eötvös Lorand University, Hungary

    Andras Sárközy

  7. Universität Dortmund, Germany

    Ingo Wegener

  8. University of Southern California, Los Angeles, USA

    Zhen Zhang

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Dodunekov, S., Simonis, J. (2000). Constructions of Optimal Linear Codes. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_21

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  • DOI: https://doi.org/10.1007/978-1-4757-6048-4_21

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4967-7

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