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Resolution of a Conjecture on the Covering Radius of Linear Codes
The covering radius of a q-ary block code C of length n is defined as the smallest integer...
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Saturating systems and the rank-metric covering radius
We introduce the concept of a rank-saturating system and outline its correspondence to a rank-metric code with a given covering radius. We consider...
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The covering radius of permutation designs
A notion of t -designs in the symmetric group on n letters was introduced by Godsil in 1988. In particular, t -transitive sets of permutations form a t -...
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Computing the Covering Radius of a Polytope with an Application to Lonely Runners
We study the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation...
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The Covering Radius and a Discrete Surface Area for Non-Hollow Simplices
We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of d /2 in...
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Linear Programming Bounds for Covering Radius of Spherical Designs
We apply polynomial techniques (i.e., techniques which invole polynomials) to obtain lower and upper bounds on the covering radius of spherical...
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Asymptotic Distributions of Covering and Separation Measures on the Hypersphere
We consider measures of covering and separation that are expressed through maxima and minima of distances between points of an hypersphere. We...
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Flows and Covering Spaces
The thesis of this book is that covering spaces provide a suitable modern setting for a unified presentation of the structure of flows on compact...
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Worst-Case Optimal Covering of Rectangles by Disks
We provide the solution for a fundamental problem of geometric optimization by giving a complete characterization of worst-case optimal disk...
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A Local Search Algorithm for Radius-Constrained k-Median
Given a set X of n points in a metric space and a radius R, we consider the combining version of k-center and k-median which is with the same...
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The Radius of Metric Regularity Revisited
The paper extends the radius of metric regularity theorem by Dontchev, Lewis and Rockafellar (2003) by providing an exact formula for the radius with...
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A Cap Covering Theorem
A cap of spherical radius α on a unit d -sphere S is the set of points within spherical distance α from a given point on the sphere. Let
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Covering Spaces
At this stage we are only able to show that certain spaces are simply connected: normally it’s quite difficult to prove directly the existence of...
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Influence of Concavity of Liquid Layer Covering a Target on High-Speed Liquid Impact
AbstractIn some cases of collapse of a toroidal bubble near a wall, the impact of the jet, penetrating the bubble, on the bubble side closest to the...
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Space Exploration: Partial Covering and Quantization
The main developments in this chapter are:...
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On the Steklov spectrum of covering spaces and total spaces
We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the...
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