Lattices with exponentially large kissing numbers

We construct a sequence of lattices ${L_{n_{i}} \subset ℝ^{n_{i}}}$ for $n_{i} \to \infty$ with exponentially large kissing numbers, namely, ${log}_{2} τ (L_{n_{i}}) > 0.0338 \cdot n_{i} - o (n_{i})$ . We also show that the maximum lattice kissing number $τ_{n}^{l}$ in $n$ dimensions satisfies ${log}_{2} τ_{n}^{l} > 0.0219 \cdot n - o (n)$ for any $n$ .

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Keywords

lattices, algebraic geometry codes, kissing numbers, Drinfeld modular curves

Mathematical Subject Classification 2010

Primary: 11H31, 11H71, 14G15, 52C17

Milestones

Received: 22 August 2018

Revised: 3 October 2018

Accepted: 18 October 2018

Published: 20 May 2019

Authors

Serge Vlăduţ
Aix Marseille Université, CNRS Centrale Marseille I2M UMR 7373 Marseille France	IITP RAS Moscow Russia

Vol. 8, No. 2, 2019

Serge Vlăduţ

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors