Constructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields

  • B. A. Sethuraman
  • Frédérique Oggier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


We describe some constructions of orthonormal lattices in totally real subfields of cyclotomic fields, obtained by endowing their ring of integers with a trace form. We also describe constructions of quaternion division algebras over such fields. Orthonormal lattices and quaternion division algebras over totally real fields find use in wireless networks in ultra wideband communication, and we describe the application.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • B. A. Sethuraman
    • 1
  • Frédérique Oggier
    • 2
  1. 1.Department of Mathematics, California State University, Northridge 
  2. 2.Department of Electrical Engineering, California Institute of Technology 

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