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Flat tori, lattices and bounds for commutative group codes
(SPRINGER, 2008)
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 ...
Quasi-Perfect Codes From Cayley Graphs Over Integer Rings
(Ieee-inst Electrical Electronics Engineers IncPiscatawayEUA, 2013)
Topological quantum codes from lattices partition on the n-dimensional flat tori
(2021-08-01)
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 ...