Journal of Algebraic Combinatorics

, Volume 45, Issue 1, pp 129–148 | Cite as

Families of optimal packings in real and complex Grassmannian spaces



A construction based on a \(4l \times 4l\) Hadamard matrix leads to a new family of optimal orthoplex packings in Grassmannian spaces \(G_{\mathbb {R}}(8l, 4l)\) and \(G_{\mathbb {C}}(4l, 2l)\). A related construction gives an optimal simplex packings in \(G_{\mathbb {R}}(8 l-1, 4 l - 1)\) and \(G_{\mathbb {R}}(8l-1, 4l)\) with the additional assumption of an \(8l \times 8l\) skew Hadamard matrix and a related 1-factorization of a complete graph. A construction of a maximal optimal simplex packings in \(G_{\mathbb {C}}(2l-1, l- 1)\) and \(G_{\mathbb {C}}(2l-1,l)\) is given.


Grassmannian packings Optimal packings Hadamard matrices Rankin bound Chordal distance Space-time codes 

Mathematics Subject Classification

Primary 51F25 51M20 52C17 Secondary 15A30 15B34 94B60 14M15 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia
  2. 2.INRIA Lille - Nord Europe, SequeL teamVilleneuve d’AscqFrance

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