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Harmonic Index Designs in Binary Hamming Schemes

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Abstract

We recall the “addition formula” for a commutative association scheme. From this formula we construct a linear programming for the size of harmonic index designs and define the notion of tight designs using Fisher type inequality. We examine the existence of tight harmonic index T-designs for some T in binary Hamming association schemes H(d, 2).

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Acknowledgements

We thank the referees for helpful comments which lead to the improvement of the paper. In the original version, the cases of \(\{ 2 \}\)- and \(\{ 4,2 \}\)-designs were not explicitly mentioned. Eiichi Bannai was supported in part by NSFC Grant No. 11271257.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai, China

    Yan Zhu & Eiichi Bannai

  2. Misakigaoka 2-8-21, Itoshima-shi, Fukuoka, 819-1136, Japan

    Etsuko Bannai

  3. Faculty of Law, Kobe Gakuin University, Minatojima, Chuo-ku, Kobe, 650-8586, Japan

    Takuya Ikuta

  4. Sogang research team for discrete and geometric structures, Sogang University, Mapo-gu, Seoul, 04107, Korea

    Kyoung-Tark Kim

Authors
  1. Yan Zhu
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  2. Eiichi Bannai
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  3. Etsuko Bannai
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  4. Takuya Ikuta
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  5. Kyoung-Tark Kim
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Correspondence to Kyoung-Tark Kim.

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Zhu, Y., Bannai, E., Bannai, E. et al. Harmonic Index Designs in Binary Hamming Schemes. Graphs and Combinatorics 33, 1405–1418 (2017). https://doi.org/10.1007/s00373-017-1784-5

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  • DOI: https://doi.org/10.1007/s00373-017-1784-5

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