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International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 1999: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 231–244Cite as

Quantum Reed—Solomon Codes

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

Abstract

We introduce a new class of quantum error—correcting codes derived from (classical) Reed—Solomon codes over finite fields of characteristic two. Quantum circuits for encoding and decoding based on the discrete cyclic Fourier transform over finite fields are presented.

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Author information

Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme Arbeitsgruppe Quantum Computing, Universität Karlsruhe, Am Fasanengarten 5, 76 128, Karlsruhe, Germany

    Markus Grassl, Willi Geiselmann & Thomas Beth

Authors
  1. Markus Grassl
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  2. Willi Geiselmann
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  3. Thomas Beth
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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Grassl, M., Geiselmann, W., Beth, T. (1999). Quantum Reed—Solomon Codes. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_23

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  • DOI: https://doi.org/10.1007/3-540-46796-3_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

  • eBook Packages: Springer Book Archive

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