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# Orthogonality defect and coherence of cyclotomic lattices (Lenny Fukshansky, CMC)

## February 7, 2023 @ 12:15 pm - 1:10 pm

There are two different measures of how far a given Euclidean lattice is from being orthogonal — the orthogonality defect and the average coherence. The first of these comes from the study of sphere packing while the second is motivated by frame theory, but both of them have applications in digital communications, especially in coding theory and cryptography. It is interesting to understand how the two are related. We investigate this question on an important class of cyclotomic lattices, where some nice formulas can be derived and certain empirical observations can be made. Joint work with David Kogan.