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On Self-dual Codes over Z 16

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5527))

Abstract

In this paper, we look at self-dual codes over the ring Z 16 of integers modulo 16. From any doubly even self-dual binary code, we construct codes over Z 16 and give a necessary and sufficient condition for the self-duality of induced codes. We then give an inductive algorithm for constructing all self-dual codes over Z 16 , and establish the mass formula, which counts the number of such codes.

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References

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Author information

Authors and Affiliations

  1. Department of Business Studies and Informatics, Daito Bunka University, Tokyo, Japan

    Kiyoshi Nagata

  2. Institute of Mathematics, University of the Philippines, Quezon City, Philippines

    Fidel Nemenzo

  3. Faculty of Science and Technology, Sophia University, Tokyo, Japan

    Hideo Wada

Authors
  1. Kiyoshi Nagata
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  2. Fidel Nemenzo
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  3. Hideo Wada
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Editor information

Editors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans, 26, 43007, Tarragona, Spain

    Maria Bras-Amorós

  2. Department of Mathematics, The Technical University of Denmark, Building 303, 2800, Lyngby, Denmark

    Tom Høholdt

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© 2009 Springer-Verlag Berlin Heidelberg

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Nagata, K., Nemenzo, F., Wada, H. (2009). On Self-dual Codes over Z 16 . In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-02181-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02180-0

  • Online ISBN: 978-3-642-02181-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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