Dense Circulant Lattices From Nonlinear Systems

11/15/2021

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by   William Lima da Silva Pinto, et al.

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Circulant lattices are those with a circulant generator matrix. They can be described by a basis containing a vector and its circular shifts. In this paper, we present certain conditions under which the norm expression of an arbitrary vector of a circulant lattice is substantially simplified, and then investigate some of the lattices obtained under these conditions. We exhibit systems of nonlinear equations whose solutions yield lattices as dense as D_n in odd dimensions.