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Archiv der Mathematik

, Volume 112, Issue 2, pp 139–148 | Cite as

Well-rounded algebraic lattices in odd prime dimension

  • Robson R. de AraujoEmail author
  • Sueli I. R. Costa
Article
  • 13 Downloads

Abstract

Well-rounded lattices have been considered in coding theory, in approaches to MIMO, and SISO wiretap channels. Algebraic lattices have been used to obtain dense lattices and in applications to Rayleigh fading channels. Recent works study the relation between well-rounded lattices and algebraic lattices, mainly in dimension two. In this article we present a construction of well-rounded algebraic lattices in Euclidean spaces of odd prime dimension. We prove that for each Abelian number field of odd prime degree having squarefree conductor, there exists a \({\mathbb {Z}}\)-module M such that the canonical embedding applied to M produces a well-rounded lattice. It is also shown that for each odd prime dimension there are infinitely many non-equivalent well-rounded algebraic lattices, with high indexes as sublattices of other algebraic lattices.

Keywords

Lattices Minkowski embedding Well-rounded lattices 

Mathematics Subject Classification

11H06 11H71 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Mathematics, University of CampinasCampinasBrazil

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