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Existence on Splitting-Balanced Block Designs with Resolvability

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Abstract

The concept of splitting-balanced block designs (SBD) was defined with some applications for authentication codes by Ogata, Kurosawa, Stinson and Saido. The existence of SBDs has been discussed through direct and recursive constructions in literature. In this paper, we focus on the property of resolvability in a SBD, and two improved bounds for the number of blocks in SBDs with resolvability are presented. Furthermore, some equivalence between SBDs with resolvability and other combinatorial designs are provided. Finally existence results of some classes of SBDs with resolvability are shown by use of recursive constructions and available results on other combinatorial structures.

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Acknowledgements

The authors wish to thank the referee for the constructive comments and suggestions.

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Authors and Affiliations

  1. Chuo Gakuin University, Chiba, 270-1196, Japan

    Kazuki Matsubara

  2. Kobe University, Hyogo, 657-8501, Japan

    Masanori Sawa

  3. Tokyo University of Science, Tokyo, 162-8601, Japan

    Sanpei Kageyama

Authors
  1. Kazuki Matsubara
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  2. Masanori Sawa
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  3. Sanpei Kageyama
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Correspondence to Kazuki Matsubara.

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Matsubara, K., Sawa, M. & Kageyama, S. Existence on Splitting-Balanced Block Designs with Resolvability. Graphs and Combinatorics 33, 561–572 (2017). https://doi.org/10.1007/s00373-017-1777-4

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  • DOI: https://doi.org/10.1007/s00373-017-1777-4

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