Abstract:We introduce maximal and average coherence on lattices by analogy with these
notions on frames in Euclidean spaces. Lattices with low coherence can be of
interest in signal processing, whereas lattices with high orthogonality defect
are of interest in sphere packing problems. As such, coherence and
orthogonality defect are different measures of the extent to which a lattice
fails to be orthogonal, and maximizing their quotient (normalized for the
number of minimal vectors with respect to dimension) gives latti… Show more
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