Lattices from Codes

  • Sueli I. R. Costa
  • Frédérique Oggier
  • Antonio Campello
  • Jean-Claude Belfiore
  • Emanuele Viterbo
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


A natural way of constructing lattices is from error-correcting codes, using the so-called Construction A. It associates a lattice in \(\mathbb {R}^{n}\) to a linear code in \(\mathbb {Z}_{q}^{n}\) (the set \(\mathbb {Z}_{q}\) of integers modulo q will be introduced next). Such lattices are also called q-ary lattices (or modulo-q lattices) and have several applications in information theory and cryptography.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Sueli I. R. Costa
    • 1
  • Frédérique Oggier
    • 2
  • Antonio Campello
    • 3
  • Jean-Claude Belfiore
    • 4
  • Emanuele Viterbo
    • 5
  1. 1.Institute of Mathematics, Statistics and Computer ScienceUniversity of CampinasCampinasBrazil
  2. 2.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  3. 3.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK
  4. 4.Communications and Electronics DepartmentTélécom ParisTechParisFrance
  5. 5.Department of Electrical and Computer Systems EngineeringMonash UniversityClaytonAustralia

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