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Almost \(2\)-perfect \(6\)-cycle systems

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Abstract

We prove that an almost \(2\)-perfect \(6\)-cycle system of order \(n\) exists if and only if \(n \equiv 1\) or \(9\ (mod\ 12)\), and that an almost \(2\)-perfect maximum packing with \(6\)-cycles of order \(n\) exists for all \(n \ge 6\).

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Acknowledgments

The research of the third author was supported by NSERC of Canada Grant No. A7268.

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Authors and Affiliations

  1. Auburn University, Auburn, AL, USA

    Charles C. Lindner

  2. AGH University of Science and Technology, Kraków, Poland

    Mariusz Meszka

  3. McMaster University, Hamilton, ON, Canada

    Alexander Rosa

Authors
  1. Charles C. Lindner
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  2. Mariusz Meszka
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  3. Alexander Rosa
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Corresponding author

Correspondence to Charles C. Lindner.

Additional information

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Cryptography, Codes, Designs and Finite Fields: In Memory of Scott A. Vanstone”.

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Lindner, C.C., Meszka, M. & Rosa, A. Almost \(2\)-perfect \(6\)-cycle systems. Des. Codes Cryptogr. 77, 321–333 (2015). https://doi.org/10.1007/s10623-015-0049-7

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  • DOI: https://doi.org/10.1007/s10623-015-0049-7

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