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Designs, Codes and Cryptography

, Volume 73, Issue 3, pp 983–996 | Cite as

New binary self-dual codes of lengths 50–60

  • Nikolay Yankov
  • Moon Ho Lee
Article

Abstract

Using 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 \([50+2t,25+t]\) codes having an automorphism of order 5 for \(t=0,\dots ,5\). As a consequence, we determine the weight enumerators for which there is an optimal binary self-dual \([52, 26, 10]\) code. Some of the constructed codes for lengths 52, 54, 58, and 60 have new values for the parameter in their weight enumerator. We also construct more than 3,000 new doubly-even \([56,28,12]\) self-dual codes.

Keywords

Self-dual codes Automorphism Classification 

Mathematics Subject Classification

94B05 11T71 

Notes

Acknowledgments

We thank the anonymous referees for the helpful comments and suggestions, which significantly contributed to improving the quality of the publication. This paper was studied 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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