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On constructions and parameters of symmetric configurations \(v_{k}\)

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Abstract

The spectrum of possible parameters of symmetric configurations is investigated. We propose some new constructions, mainly based on Finite Geometry and on extension methods. New parameters are provided, both for general symmetric configurations and for cyclic symmetric configurations. For several values of \(k\), new upper bounds on the minimum integer \(E\) such that for each \(v\ge E\) there exists a (cyclic) symmetric configuration \(v_{k}\) are obtained.

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Notes

  1. The authors of the papers [5, 6] (represented here by Davydov) regret that the paper [22] is not cited in [5, 6]; the reason is that, unfortunately, the authors did not know the paper [22] during the preparation of [5, 6].

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Acknowledgments

The authors would like to thank one of the anonymous referees for his/her helpful comments and remarks, and for bringing to our attention papers [3, 10]. The research of G. Faina, M. Giulietti, S. Marcugini, and F. Pambianco was supported by Ministry for Education, University and Research of Italy (MIUR) (Project “Geometrie di Galois e strutture di incidenza”, PRIN 2009–2010) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA—INdAM). The research of A.A. Davydov was carried out at the IITP RAS at the expense of the Russian Foundation for Sciences (Project 14-50-00150)

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Correspondence to Fernanda Pambianco.

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Communicated by J. H. Koolen.

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Davydov, A.A., Faina, G., Giulietti, M. et al. On constructions and parameters of symmetric configurations \(v_{k}\) . Des. Codes Cryptogr. 80, 125–147 (2016). https://doi.org/10.1007/s10623-015-0070-x

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