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Long Extended BCH Codes Are Spanned by Minimum Weight Words

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3857))

Abstract

It is shown that long enough extended t-error correcting BCH codes B t are spanned by its lightest words of weight 2t + 2. The proof follows from an upper bound on the number of words of weight 2t + 2 in any subcode of B t of codimension 1.

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Author information

Authors and Affiliations

  1. MIT Computer Science and Artificial Intelligence Laboratory (CSAIL), 32 Vassar Street, Cambridge, MA, 02139, USA

    Tali Kaufman

  2. Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv, 69978, Israel

    Simon Litsyn

Authors
  1. Tali Kaufman
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  2. Simon Litsyn
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, Honolulu, USA

    Marc P. C. Fossorier

  2. National Institute of Advanced Industrial Science and Technology (AIST), Research Center for Information Security (RCIS),  

    Hideki Imai

  3. Department of Electrical and Computer Engineering, University of California, CA 95616, Davis,  

    Shu Lin

  4. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

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© 2006 Springer-Verlag Berlin Heidelberg

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Kaufman, T., Litsyn, S. (2006). Long Extended BCH Codes Are Spanned by Minimum Weight Words. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_28

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  • DOI: https://doi.org/10.1007/11617983_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31423-3

  • Online ISBN: 978-3-540-31424-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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