Zobrazeno 1 - 10
of 1 506
pro vyhledávání: '"Kissing number"'
In this note, we present examples showing that several natural ways of constructing lattices from error-correcting codes do not in general yield a correspondence between minimum-weight non-zero codewords and shortest non-zero lattice vectors. From th
Externí odkaz:
http://arxiv.org/abs/2410.16660
Autor:
Boyvalenkov, Peter, Cherkashin, Danila
We prove that the kissing number in 48 dimensions among antipodal spherical codes with certain forbidden inner products is 52\,416\,000. Constructions of attaining codes as kissing configurations of minimum vectors in even unimodular extremal lattice
Externí odkaz:
http://arxiv.org/abs/2312.05121
Akademický článek
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Autor:
Mendelsohn, Andrew
We obtain an inequality for the kissing number in 16 dimensions. We do this by generalising a sum-product bound of Solymosi and Wong for quaternions to a semialgebra in dimension 16. In particular, we obtain the inequality $$k_{16}\geq \frac{\sum_{x
Externí odkaz:
http://arxiv.org/abs/2303.03515
The average kissing number of $\mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $\mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite
Externí odkaz:
http://arxiv.org/abs/2003.11832
Autor:
Dostert, Maria, Kolpakov, Alexander
Publikováno v:
Math. Comp. (2021)
This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in hyperbolic $\mathbb{H}^n$ and spherical $\mathbb{S}^n$ spaces, for $n\geq 2$. For that purpose, the kissing number is replaced by the kissing func
Externí odkaz:
http://arxiv.org/abs/2003.05547
Autor:
Glazyrin, Alexey
In this note, we give a short solution of the kissing number problem in dimension three.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2012.15058
Autor:
Dória, Cayo, Murillo, Plinio G. P.
In this article we construct a sequence $\{M_i\}$ of non compact finite volume hyperbolic $3$-manifolds whose kissing number grows at least as $\mathrm{vol}(M_i)^{\frac{31}{27}-\epsilon}$ for any $\epsilon>0$. This extends a previous result due to Sc
Externí odkaz:
http://arxiv.org/abs/2003.01863
Autor:
Dostert, Maria, Kolpakov, Alexander
This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $\mathbb{H}^n$, for $n\geq 2$. For that purpose, the kissing number is replaced by the kissing function $\kappa(n, r)$ which depends on the radius
Externí odkaz:
http://arxiv.org/abs/1907.00255
Akademický článek
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