On spherical codes generating the kissing number in dimensions 8 and 24
type: Item
instance of: scholarly article
title: On spherical codes generating the kissing number in dimensions 8 and 24
zbMATH Open document ID: 0760.94015
DOI: 10.1016/0012-365X(92)90547-S
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: A spherical code is a subset of the unit sphere in \(\mathbb{R}^ n\). It is interesting to find a spherical code with many codewords given that two different words are at distance at least \(\rho\). The determination of the size of a maximum \(n\)-dimensional spherical code with \(\rho=1\) is equivalent to finding the kissing number \(\tau_ n\), that is, the largest possible number of equal size spheres that can touch a sphere in \(\mathbb{R}^ n\). The authors propose three methods (one of them well-known) for constructing a spherical code in \(\mathbb{R}^ n\) from binary error correcting codes. With a judicious choice of such binary codes, (and some additional work showing that the union of some constructed spherical codes still have large minimum distance), spherical codes with \(\tau_ 8\) and \(\tau_{24}\) words are constructed. As building blocks, the \([8,4,4]\) Hamming code and the \([24,12,8]\) Golay code are used.
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 94525
zbMATH Keywords: spherical code
zbMATH Keywords: kissing number
zbMATH Keywords: minimum distance
zbMATH Keywords: Hamming code
zbMATH Keywords: Golay code
author: Thomas Ericson
author: Victor A. Zinoviev
reviewed by: L. M. G. M. Tolhuizen
MaRDI profile type: Publication
cites work: Q4039784
cites work: The Closest Packing of Spherical Caps in n Dimensions
cites work: Notes on Sphere Packings
cites work: Q3665801
cites work: New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
cites work: Q4733831
cites work: Multidimensional signals for a continuous channel
cites work: EUROCODE '90. International Symposium on Coding Theory and Applications, Udine, Italy, November 5-9, 1990. Proceedings
full work available at URL: 0012-365x(92)90547-s
OpenAlex ID: W1977188635
Wikidata QID: Q127186720
description: scientific article; zbMATH DE number 94525