Designs, Codes and Cryptography

, Volume 79, Issue 1, pp 171–182 | Cite as

On the automorphisms of order 15 for a binary self-dual \([96, 48, 20]\) code

  • Stefka Bouyuklieva
  • Wolfgang Willems
  • Nikolay Yankov
Article
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Abstract

The structure of the binary self-dual codes invariant under the action of a cyclic group of order \(pq\) for odd primes \(p\ne q\) is considered. As an application we prove the nonexistence of an extremal self-dual \([96, 48, 20]\) code with an automorphism of order \(15\) which closes a gap in de la Cruz and Willems (IEEE Trans Inf Theory 57:6820–6823, 2011).

Keywords

Self-dual codes Doubly-even codes Automorphisms 

Mathematics Subject Classification

94B05 20B25 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Stefka Bouyuklieva
    • 1
  • Wolfgang Willems
    • 2
  • Nikolay Yankov
    • 3
  1. 1.Faculty of Mathematics and InformaticsVeliko Tarnovo UniversityVeliko TarnovoBulgaria
  2. 2.Otto-von-Guericke UniversitätMagdeburgGermany
  3. 3.Faculty of Mathematics and InformaticsShumen UniversityShumenBulgaria

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