scholarly journals Finite sphere packing and sphere covering

1989 ◽  
Vol 4 (1) ◽  
pp. 19-40 ◽  
Author(s):  
G. Fejes Tóth ◽  
P. Gritzmann ◽  
J. M. Wills
Keyword(s):  
Sphere Packing ◽  
Sphere Covering ◽  
Finite Sphere

scholarly journals NETWORK CODING WITH MODULAR LATTICES

2011 ◽  
Vol 10 (06) ◽  
pp. 1319-1342 ◽  
Author(s):  
ANDREAS KENDZIORRA ◽  
STEFAN E. SCHMIDT
Keyword(s):  
Vector Space ◽  
Network Coding ◽  
Sphere Packing ◽  
Height Function ◽  
Error Correcting Codes ◽  
Modular Lattices ◽  
Subspace Lattice ◽  
New Model ◽  
Singleton Bound ◽  
Sphere Covering

Kötter and Kschischang presented in 2008 a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d : (U, V) ↦ dim (U+V)- dim (U∩V). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map d : (u, v) ↦ h(u ∨ v) - h(u ∧ v), where h is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a Singleton bound for codes, which are subsets of modular lattices.

Combinatorial Materials Development using Gradient Arrays. Sphere Covering Lattice Designs: Designs for Efficient use of Experimental Resources.

2003 ◽  
Vol 804 ◽  
Author(s):  
James N. Cawse
Keyword(s):  
High Throughput ◽  
Combinatorial Chemistry ◽  
Sphere Packing ◽  
Materials Development ◽  
Packing And Covering ◽  
Higher Dimensional ◽  
Combinatorial Materials ◽  
Sphere Covering ◽  
The Cost

ABSTRACTGradient arrays are now common tools in combinatorial chemistry for discovery of new leads to commercial materials. Although the cost per sample has dropped markedly with new high throughput methods, efficient use of experimental resources is still important. Examination of gradient arrays from an informational standpoint suggests that designs which use the concepts of sphere packing and covering will be more efficient than simple gradients. This is especially true in higher dimensional systems.

Bounds on subspace codes based on totally isotropic subspace in symplectic spaces and extended symplectic spaces

2019 ◽  
Vol 12 (05) ◽  
pp. 1950069
Author(s):  
Mahdieh Hakimi Poroch
Keyword(s):  
Sphere Packing ◽  
Symplectic Space ◽  
Isotropic Subspace ◽  
Subspace Codes ◽  
Singleton Bound ◽  
Symplectic Spaces ◽  
Isotropic Subspaces ◽  
Totally Isotropic Subspace ◽  
Totally Isotropic Subspaces

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].

Dense Sphere Packing in the NaZn13 Structure Type

2010 ◽  
Vol 114 (33) ◽  
pp. 14013-14017 ◽  
Author(s):  
Toby S. Hudson
Keyword(s):  
Sphere Packing ◽  
Structure Type

Unequal-Sphere Packing Model for Simulation of the Uniaxially Compressed Iodine Adlayer on Au(111)

2005 ◽  
Vol 109 (46) ◽  
pp. 21710-21715 ◽  
Author(s):  
Alexandre Tkatchenko ◽  
Nikola Batina
Keyword(s):  
Sphere Packing ◽  
Packing Model
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