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Self-dual Codes over Small Prime Fields from Combinatorial Designs

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Algebraic Informatics (CAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5725))

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Abstract

In this paper, we give some new extremal ternary self-dual codes which are constructed by skew-Hadamard matrices. This has been achieved with the aid of a recently presented modification of a known construction method. In addition, we survey the known results for self-dual codes over GF(5) constructed via combinatorial designs, i.e. Hadamard and skew-Hadamard matrices, and we give a new self-dual code of length 72 and dimension 36 whose minimum weight is 16 over GF(5) for the first time. Furthermore, we give some properties of the generated self-dual codes interpreted in terms of algebraic coding theory, such as the orders of their automorphism groups and the corresponding weight enumerators.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Zografou, 15773, Athens, Greece

    Christos Koukouvinos & Dimitris E. Simos

Authors
  1. Christos Koukouvinos
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  2. Dimitris E. Simos
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Editors and Affiliations

  1. Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Symeon Bozapalidis

  2. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    George Rahonis

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Koukouvinos, C., Simos, D.E. (2009). Self-dual Codes over Small Prime Fields from Combinatorial Designs. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2009. Lecture Notes in Computer Science, vol 5725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03564-7_18

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  • DOI: https://doi.org/10.1007/978-3-642-03564-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03563-0

  • Online ISBN: 978-3-642-03564-7

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