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Designs, Codes and Cryptography

, Volume 80, Issue 1, pp 125–147 | Cite as

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

  • Alexander A. Davydov
  • Giorgio Faina
  • Massimo Giulietti
  • Stefano Marcugini
  • Fernanda Pambianco
Article

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.

Keywords

Configurations in combinatorics Symmetric configurations  Cyclic configurations Golomb rulers Projective geometry LDPC codes 

Mathematics Subject Classification

05C10 05B25 94B05 

Notes

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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Alexander A. Davydov
    • 1
  • Giorgio Faina
    • 2
  • Massimo Giulietti
    • 2
  • Stefano Marcugini
    • 2
  • Fernanda Pambianco
    • 2
  1. 1.Institute for Information Transmission Problems (Kharkevich Institute)Russian Academy of SciencesMoscowRussian Federation
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaPerugiaItaly

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