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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