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Designs, Codes and Cryptography

, Volume 74, Issue 3, pp 571–579 | Cite as

Classification of self-dual codes of length 50 with an automorphism of odd prime order

  • Nikolay Yankov
  • Moon Ho Lee
Article

Abstract

By applying a method for constructing binary self-dual codes with an automorphism of odd prime order \(p\), we give a full classification of all optimal binary self-dual codes of length 50 having an automorphism of order 3. As a consequence, we give a full classification of all \([50, 25, 10]\) codes possessing an automorphism of odd prime order. Up to equivalence, there are exactly 177,601 such codes. This completely determines all possibilities for the cardinality of the automorphism group of such a code. Also, we show that there are at least 52 non-isomorphic quasi-symmetric 2-(49, 9, 6) designs, derived from the \([50,25,10]\) codes with a particular weight enumerator.

Keywords

Automorphisms Classification Self-dual codes  Quasi-symmetric designs 

Mathematics Subject Classification

94B05 11T71 

Notes

Acknowledgments

We thank the anonymous referees for the comments and suggestions, which contributed to improving the quality of the publication. This paper was written with the support of the Ministry of Education Science and Technology (MEST) and the Korean Federation of Science and Technology Societies (KOFST). This work was also supported by World Class University Project (WCU) R-32-2012-000-20014-0, Basic Science Research Program 2010-0020942, NRF Korea, and MEST 2012-002521, NRF Korea. The first author was also supported by Shumen University under Grant RD-08-245/13.03.2013.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsShumen UniversityShumenBulgaria
  2. 2.Division of Electronics & Information EngineeringChonbuk National UniversityJeonju CitySouth Korea

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