A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Covering and Packing in Linear Space
[chapter]

2010
*
Lecture Notes in Computer Science
*

Can one improve these bounds to only

doi:10.1007/978-3-642-14165-2_61
fatcat:udxf6oa5onclxk5p6yyrygxnxy
*linear**in*the size of the family? Here, we answer the question*in*the affirmative regarding the*space*requirement, while not increasing the time requirement. ... When the size of the family is exponential*in*n, the fastest known algorithms for these problems use inclusion-exclusion*and*fast zeta transform, taking time*and**space*2 n , up to a factor polynomial*in*... This bottleneck can be removed by taking a more balanced scheme with n 1*and*n 2 about equal, yielding time*and**space*O * (2 n/2 ) for each of the O * (2 n/2 ) processors. ...##
###
Covering and packing in linear space

2011
*
Information Processing Letters
*

Can one improve these bounds to only

doi:10.1016/j.ipl.2011.08.002
fatcat:rj32rkvxknefnerpdocpregzy4
*linear**in*the size of the family? Here, we answer the question*in*the affirmative regarding the*space*requirement, while not increasing the time requirement. ... When the size of the family is exponential*in*n, the fastest known algorithms for these problems use inclusion-exclusion*and*fast zeta transform, taking time*and**space*2 n , up to a factor polynomial*in*... This bottleneck can be removed by taking a more balanced scheme with n 1*and*n 2 about equal, yielding time*and**space*O * (2 n/2 ) for each of the O * (2 n/2 ) processors. ...##
###
Page 9329 of Mathematical Reviews Vol. , Issue 2003m
[page]

2003
*
Mathematical Reviews
*

This is a brief survey article

*in*which the author reviews the main results, methods,*and*some open problems about simultaneous*packing**and**covering**in*Euclidean n-*space*. ... One of the basic problems*in*the theory of*packing**and**covering*is to determine, for a given positive integer k, the minima! ...##
###
Duality between packings and coverings of the Hamming space

2005
*
IEEE Information Theory Workshop, 2005.
*

We investigate the

doi:10.1109/itw.2005.1531849
dblp:conf/itw/CohenV05
fatcat:chqejnfnr5aqtpk43qiiqi7y3i
*packing**and**covering*densities of*linear**and*nonlinear binary codes,*and*establish a number of duality relationships between the*packing**and**covering*problems. ... Specifically, we prove that if almost all codes (*in*the class of*linear*or nonlinear codes) are good*packings*, then only a vanishing fraction of codes are good*coverings*,*and*vice versa: if almost all ... Vice versa, if almost all codes*in*C (n, M + 1) are good*packings*, then almost all codes*in*C (n, M ) are bad*coverings*. Ã The same is true for*linear*codes. ...##
###
Duality between Packings and Coverings of the Hamming Space
[article]

2005
*
arXiv
*
pre-print

We investigate the

arXiv:cs/0507015v1
fatcat:6drgx35r5zhl3fq53ba6svds5u
*packing**and**covering*densities of*linear**and*nonlinear binary codes,*and*establish a number of duality relationships between the*packing**and**covering*problems. ... Specifically, we prove that if almost all codes (*in*the class of*linear*or nonlinear codes) are good*packings*, then only a vanishing fraction of codes are good*coverings*,*and*vice versa: if almost all ... We are grateful to Alexander Barg*and*Ilya Dumer for helpful discussions. We are especially indebted to Ilya Dumer for sending us his proof*in*[6]. ...##
###
Packing and covering in higher dimensions
[article]

2022
*
arXiv
*
pre-print

The present work surveys problems

arXiv:2202.11358v1
fatcat:nekz37kvhnfmrbr3gsrfjushje
*in*n-dimensional*space*with n large. Early development*in*the study of*packing**and**covering**in*high dimensions was motivated by the geometry of numbers. ... Subsequent results, such as the discovery of the Leech lattice*and*the*linear*programming bound, which culminated*in*the recent solution of the sphere*packing*problem*in*dimensions 8*and*24, were influenced ... The excellent book of Rogers [1964] gives an exhaustive account of*packing**and**covering**in*high dimensions. ...##
###
Packing And Covering Radii Of Linear Error-Block Codes

2013
*
Zenodo
*

The purpose of this paper is to generalize some results on the

doi:10.5281/zenodo.1088269
fatcat:jbus752rxnbw3pm6qayui65ixe
*packing**and*the*covering*radii to the error-block case. ... We study their properties when a code undergoes some specific modifications*and*combinations with another code. We give a few bounds on the*packing**and*the*covering*radii of these codes. ...*In*this paper, we extend the definitions of*packing**and**covering*radii to*linear*error-block codes. ...##
###
Packing and Covering δ-Hyperbolic Spaces by Balls
[chapter]

2007
*
Lecture Notes in Computer Science
*

We consider the problem of

doi:10.1007/978-3-540-74208-1_5
fatcat:w4kjwnfjjveppht6iu7o7tdvyu
*covering**and**packing*subsets of δ-hyperbolic metric*spaces**and*graphs by balls. ... This result is established*in*the general framework of δ-hyperbolic geodesic metric*spaces**and*is extended to some other set families derived from balls. ...*In*this note, we consider the problem of*covering**and**packing*by balls*and*union of balls of hyperbolic metric*spaces**and*graphs. ...##
###
Page 4168 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
*
Mathematical Reviews
*

88h:5 1021
51N Analytic

*and*descriptive geometry See also 14053, 30021, 51017. 88h:51021 51N15 Somer, Josef (CS-CVUTE)*Linear*projective motions*in**spaces*of finite dimension. (Czech. ... Kemnitz, Characterization of cen- trally symmetric convex domains*in*planes of constant curvature (pp. 179-189); A. Florian,*Packing**and**covering*with convex discs (pp. 191-207); Richard K. ...##
###
Linear Programming Bounds for Codes via a Covering Argument

2008
*
Discrete & Computational Geometry
*

, on optimal

doi:10.1007/s00454-008-9128-0
fatcat:ugze4mafhfgttm4uhf3p7jm5ua
*packing*of Hamming balls*in*a Hamming cube. ... We recover the first*linear*programming bound of McEliece, Rodemich, Rumsey,*and*Welch for binary error-correcting codes*and*designs via a*covering*argument. ... We also thank Simon Litsyn*and*Madhu Sudan for valuable remarks. ...##
###
Page 8987 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

a three-dimensional normed

*space*, the problem of universal*coverings*for sets of unit diameter*in*a Euclidean*space*,*and*some related problems.” ... A solid*packing*of equal circles*in*either, the Euclidean plane or the sphere, is always the densest*packing*(similarly for*coverings*). ...##
###
Page 4961 of Mathematical Reviews Vol. , Issue 911
[page]

1991
*
Mathematical Reviews
*

For a lattice L

*in*an n-dimensional normed*space*X the*packing**and**covering*numbers are p(L) = 5 min{||x||: x € L \ {0}}, c(L) = max{dist(x, L): x € X}. ... (PL-LODZ) On the lattice*packing*-*covering*ratio of finite-dimensional normed*spaces*. Collog. Math. 59 (1990), no. 1, 31-33. ...##
###
Linear programming bounds for codes via a covering argument
[article]

2007
*
arXiv
*
pre-print

We recover the first

arXiv:math/0702425v1
fatcat:erel77czlnhlvpknoa5c3hatfi
*linear*programming bound of McEliece, Rodemich, Rumsey,*and*Welch for binary error-correcting codes*and*designs via a*covering*argument. ...*In*particular, we do not deal directly with Delsarte's*linear*program or orthogonal polynomial theory. ... We refer to [15, 11, 4, 14] for a detailed exposition of the notions discussed above, including error-correcting codes*and*their significance,*packing**in*metric*spaces*, association schemes, Delsarte's ...##
###
Page 976 of Mathematical Reviews Vol. 35, Issue 5
[page]

1968
*
Mathematical Reviews
*

Topics include convexity

*in*topological*linear**spaces*,*packings**and**coverings*,*and*convex bodies. ... Fejes Téth,*Packings**and**coverings**in*the plane; L. Few, Multiple*packing*of spheres: A survey; W. J. Firey, Blaschke sums of con- vex bodies*and*mixed bodies; D. ...##
###
Page 5022 of Mathematical Reviews Vol. , Issue 87i
[page]

1987
*
Mathematical Reviews
*

*In*III- V many results on finite abelian groups are proved which imply tiling,

*packing*

*and*

*covering*results for crosses

*and*semicrosses. ... Gorshkova, Unsolved groups of motions

*in*Davies

*spaces*(pp. 55-62); A. I. Egorov, Maximally moving

*spaces*of

*linear*

*and*hyperplanar elements (pp. 62-82); L. I. ...

« Previous

*Showing results 1 — 15 out of 142,495 results*