10.46298/cm.10241
https://cm.episciences.org/10241
Fukshansky, Lenny
Lenny
Fukshansky
Kogan, David
David
Kogan
On average coherence of cyclotomic lattices
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 lattices with
particularly good optimization properties. While orthogonality defect is a
fairly classical and well-studied notion on various families of lattices,
coherence is not. We investigate coherence properties of a nice family of
algebraic lattices coming from rings of integers in cyclotomic number fields,
proving a simple formula for their average coherence. We look at some examples
of such lattices and compare their coherence properties to those of the
standard root lattices.
Comment: Communications in Mathematics 31 (2023), no. 1, 57-72
episciences.org
Mathematics - Number Theory
11H06, 11H31, 11R18, 42C15
arXiv.org - Non-exclusive license to distribute
2022-11-02
2022-11-07
2022-11-07
eng
journal article
arXiv:2012.07807
10.48550/arXiv.2012.07807
2336-1298
https://cm.episciences.org/10241/pdf
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Communications in Mathematics
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