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Designs, Codes and Cryptography

, Volume 34, Issue 2–3, pp 149–153 | Cite as

Distance Regular Covers of Complete Graphs from Latin Squares

  • D. De Caen
  • D. Fon-Der-Flaass
Article

Abstract

We describe a new construction of distance regular covers of a complete graph K q 2t with fibres of size q2t-1, q a power of 2. When q=2, the construction coincides with the one found in [D. de Caen, R. Mathon, G.E. Moorhouse. J. Algeb. Combinatorics, Vol. 4 (1995) 317] and studied in [T. Bending, D. Fon-Der-Flaass, Elect. J. Combinatorics, Vol. 5 (1998) R34]. The construction uses, as one ingredient, an arbitrary symmetric Latin square of order q; so, for large q, it can produce many different covers.

Keywords

Data Structure Information Theory Complete Graph Discrete Geometry Regular Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bending, T., Fon-Der-Flaass, D. 1998Crooked functions, bent functions, and distance regular graphsElect. J. Combinatorics514R34Google Scholar
  2. A.E. Brouwer, A.M. Cohen and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, 1989. Google Scholar
  3. de Caen, D., Mathon, R., Moorhouse, G.E. 1995A family of antipodal distance-regular graphs related to the classical Preparata codesJ. Algebr. Combinatorics4317327Google Scholar
  4. C.D. Godsil, Covers of Complete Graphs. In: Progress in Algebraic Combinatorics, Adv. Stud. Pure Math., Vol. 24 (1996) pp. 137–163.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • D. De Caen
    • 1
  • D. Fon-Der-Flaass
    • 2
  1. 1.Queen’s UniversityKingstonCanada
  2. 2.Institute of MathematicsNovosibirsk 90Russia

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