In this work, we show that an n-dimensional sublattice Λ′ = mΛ of an n-dimensional lattice Λ induces a G = Znm tessellation in the flat torus Tβ′ = Rn/Λ′, where the group G is isomorphic to the lattice partition Λ/Λ′ . As ...

This paper gives a formalization for q-ary codes of the search algorithm [3] for optimum codes based on lattices and cosets [1]. With a more efficient and an automated algorithm it also has been possible to extend the ...

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a ...

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a ...

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these ...

Interference is usually viewed as an obstacle to communication in wireless networks, so we develop a new methodology to quantize the channel coefficients in order to realize interference alignment onto a 4-dimensional ...

Spherical codes in even dimensions n = 2m generated by a commutative group of orthogonal matrices can be determined by a quotient of m-dimensional lattices when the sublattice has an orthogonal basis. We discuss here the ...