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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 4/2018

26-04-2017

Combinatorial constructions of packings in Grassmannian spaces

Published in: Designs, Codes and Cryptography | Issue 4/2018

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Abstract

The problem of packing n-dimensional subspaces of m-dimensional Euclidean space such that these subspaces are as far apart as possible was introduced by Conway, Hardin and Sloane. It can be seen as a higher dimensional version of spherical codes or equiangular lines. In this paper, we first give a general construction of equiangular lines, and then present a family of equiangular lines with large size from direct product difference sets. Meanwhile, for packing higher dimensional subspaces, we give three constructions of optimal packings in Grassmannian spaces based on difference sets and Latin squares. As a consequence, we obtain many new classes of optimal Grassmannian packings.
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Metadata
Title
Combinatorial constructions of packings in Grassmannian spaces
Publication date
26-04-2017
Published in
Designs, Codes and Cryptography / Issue 4/2018
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-017-0362-4

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