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
2011 ◽  
Vol 10 (06) ◽  
pp. 1319-1342 ◽  
Author(s):  
ANDREAS KENDZIORRA ◽  
STEFAN E. SCHMIDT

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.


2003 ◽  
Vol 804 ◽  
Author(s):  
James N. Cawse

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.


2019 ◽  
Vol 12 (05) ◽  
pp. 1950069
Author(s):  
Mahdieh Hakimi Poroch

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].


2010 ◽  
Vol 114 (33) ◽  
pp. 14013-14017 ◽  
Author(s):  
Toby S. Hudson

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

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