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A framework for constructing partial geometric difference sets

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Abstract

Partial geometric difference sets (PGDSs) were defined in Olmez (J Combin Des 22(6):252–269, 2014). They are used to construct partial geometric designs. We use the framework of extended building sets to find infinite families of PGDSs in abelian groups. Included in our new families of PGDSs are generalizations of the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen difference sets.

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Notes

  1. A point-block pair (x, B) is called a flag if \(x\in B\); otherwise, it is called an antiflag.

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Acknowledgements

The authors gratefully acknowledge the generous support supplied by the Institute for Mathematical Sciences, National University of Singapore. James A. Davis acknowledges the support provided by NSA Grant H98230-16-1-0007. Oktay Olmez acknowledges the support provided by TUBITAK Research Grant Project No. 115F064.

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Authors and Affiliations

  1. Department of Math and CS, University of Richmond, Richmond, VA, 23173, USA

    James A. Davis

  2. Department of Mathematics, Faculty of Science, Ankara University, Tandoğan, 06100, Ankara, Turkey

    Oktay Olmez

Authors
  1. James A. Davis
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  2. Oktay Olmez
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Correspondence to James A. Davis.

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Communicated by J. Jedwab.

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Davis, J.A., Olmez, O. A framework for constructing partial geometric difference sets. Des. Codes Cryptogr. 86, 1367–1375 (2018). https://doi.org/10.1007/s10623-017-0400-2

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  • DOI: https://doi.org/10.1007/s10623-017-0400-2

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