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On the self-dual codes with an automorphism of order 5

  • Nikolay YankovEmail author
  • Damyan Anev
Original Paper
  • 1 Downloads

Abstract

For lengths 60,  62, and 64, by applying the method for constructing self-dual codes having an automorphism of odd prime order, we classify all optimal singly even self-dual codes with an automorphism of order 5 with 12 cycles. For the binary self-dual [62, 31, 12] codes we have found five new values of the parameter in the weight enumerator thus doubling the number of know values. For length 64 we have found codes with 14 new parameter values for both known weight enumerators. By shortening all binary self-dual [60, 30, 12] codes having an automorphism of order 5 we construct many new [58, 29, 10] self-dual codes. We have found a new value of the parameter in the weight enumerator of these codes.

Keywords

Automorphism Classification Self-dual codes Shortening 

Mathematics Subject Classification

94B05 11T71 

Notes

Acknowledgements

This work was supported by European Regional Development Fund and the Operational Program “Science and Education for Smart Growth” under Contract UNITe No. BG05M2OP001-1.001-0004-C01 (2018-2023) and by Shumen University under Project No. RD-08-115/04.02.2019. We thank the reviewers for their very helpful comments and suggestions which helped improve this work.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsKonstantin Preslavski University of ShumenShumenBulgaria

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