Designs, groups and lattices
Christine Bachoc (IMB)
TL;DR
This paper investigates Grassmannian designs within lattices, focusing on the Barnes-Wall lattices, and explores their relation to the Rankin constant, revealing that these lattices contain high-order designs.
Contribution
It demonstrates that Barnes-Wall lattices contain Grassmannian 6-designs, advancing understanding of lattice design structures and their properties.
Findings
Barnes-Wall lattices contain Grassmannian 6-designs
Connection established between lattice designs and the Rankin constant
Insights into the structure of Grassmannian designs in lattices
Abstract
We study the Grassmannian 4-designs contained in lattices, in connection with the local property of the Rankin constant. We prove that the sequence of Barnes-Wall lattices contain Grassmannian 6-designs.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Mathematical Approximation and Integration