The second minimum of Barnes-Wall lattices
Gabriele Nebe
TL;DR
This paper investigates the Barnes-Wall lattices and establishes that their second minimum is at least 1.5 times the minimum, providing insight into their geometric structure.
Contribution
It proves a lower bound for the second minimum of Barnes-Wall lattices, a novel result in lattice theory.
Findings
Second minimum is at least 1.5 times the minimum
Provides new bounds for Barnes-Wall lattice geometry
Enhances understanding of lattice minimums
Abstract
We show that the second minimum of the Barnes-Wall lattices is a least of the minimum.
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Taxonomy
TopicsAdvanced Algebra and Logic · Mathematical Approximation and Integration · Computability, Logic, AI Algorithms