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Spherical Codes from Lattices

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Abstract

Lattices are homogeneous discrete sets in the n-dimensional space that have been used in different applications in communication areas such as coding for Gaussian or fading channels and cryptography. This chapter approaches the connection between quotient of lattices and spherical codes, presenting a survey on contributions to this topic mainly based on Costa et al. (Flat tori, lattices and spherical codes. In: 2013 Information Theory and Applications Workshop (ITA), February 2013, pp 1–8), Siqueira and Costa (Des Codes Cryptogr 49(1–3):307–321, 2008), Torezzan et al. (IEEE Trans Inf Theory 59(10):6655–6663, 2013), Costa et al. (Lattice applied to codding for reliable and secure communications. Springer, 2017), and Torezzan et al. (Des Codes Cryptogr 74(2):379–394, 2015).

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Acknowledgements

The authors acknowledge all the support from IMECC-Unicamp and from FAPESP (2013/25977-7) and CNPq (312926/2013-8; 400441/2014-4) foundations. The first author wishes to thank her present and past students for their contributions on the subject discussed in this chapter.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil

    Sueli I. R. Costa

  2. School of Applied Sciences, University of Campinas, Campinas, SP, Brazil

    João E. Strapasson & Cristiano Torezzan

Authors
  1. Sueli I. R. Costa
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  2. João E. Strapasson
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  3. Cristiano Torezzan
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Corresponding author

Correspondence to Sueli I. R. Costa .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, São Paulo, Brazil

    Carlile Lavor

  2. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, São Paulo, Brazil

    Francisco A. M. Gomes

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Costa, S.I.R., Strapasson, J.E., Torezzan, C. (2018). Spherical Codes from Lattices. In: Lavor, C., Gomes, F. (eds) Advances in Mathematics and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-94015-1_5

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