Lattices with exponentially large kissing numbers

DOI10.2140/moscow.2019.8.163zbMath1448.11124arXiv1802.00886OpenAlexW3099363417WikidataQ114045351 ScholiaQ114045351MaRDI QIDQ2420496

S. G. Vleduts

Publication date: 6 June 2019

Published in: Moscow Journal of Combinatorics and Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.00886

zbMATH Keywords

Drinfeld modular curvesalgebraic geometry codeslatticeskissing numbers

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Relations with coding theory (11H71)

Related Items (9)

On kissing numbers and spherical codes in high dimensions ⋮ Kissing numbers of closed hyperbolic manifolds ⋮ Contact graphs of ball packings ⋮ On closest pair in Euclidean metric: monochromatic is as hard as bichromatic ⋮ On the lattice Hadwiger number of superballs and some other bodies ⋮ On Closest Pair in Euclidean Metric: Monochromatic is as Hard as Bichromatic ⋮ On the Number of Circuits in Regular Matroids (with Connections to Lattices and Codes) ⋮ Kissing numbers of regular graphs ⋮ Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces

Cites Work

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• Drinfeld modular curves
• Constructive high-dimensional sphere packings
• Multiplicative lattices in global fields
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• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• New Lattice Packings of Spheres
• Further lattice packings in high dimensions
• Invariants of some algebraic curves related to Drinfeld modular curves
• Linear codes with exponentially many light vectors

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