Covering radius

In mathematics, the covering radius of a collection of points P in a space is the smallest r > 0 such that spheres of radius r around the points P will completely cover the space. The term is typically used in reference to linear error-correcting codes.

Example

In the real plane, the set of all integer points (i, j) has a covering radius of $\scriptstyle \sqrt{2}/2$.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometric measurement Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу Maishofen Eugène, 11th Prince of Ligne Look at other dictionaries: Covering code — In coding theory, a covering code is an object satisfying a certain mathematical property: A code of length n over Q is an R covering code if for every word of Qn there is a codeword such that their Hamming distance is . Contents 1 Definition 2… …   Wikipedia Covering number — Not to be confused with Winding number or degree of a continuous mapping, sometimes called covering number or engulfing number . In mathematics, the ε covering number of a metric space (X, d), for some ε > 0, is the minimum… …   Wikipedia Vitali covering lemma — In mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. tatement of the lemma* Finite version: Let B {1},...,B {n} be any collection of d dimensional balls contained… …   Wikipedia Disk covering problem — The disk covering problem was proposed by C. T. Zahn in 1962. Given an integer n, the problem asks for the smallest real number r(n) such that n disks of radius r(n) can be arranged in such a way as to cover the unit disk. The best solutions to… …   Wikipedia Leech lattice — In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24 dimensional Euclidean space E24 found by John Leech (1967). Contents 1 History 2 Characterization 3 Properties …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia Lattice problem — In computer science, lattice problems are a class of optimization problems on lattices. The conjectured intractability of such problems is central to construction of secure lattice based cryptosystems. For applications in such cryptosystems,… …   Wikipedia Linear code — In mathematics and information theory, a linear code is an important type of block code used in error correction and detection schemes. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome… …   Wikipedia Error detection and correction — In mathematics, computer science, telecommunication, and information theory, error detection and correction has great practical importance in maintaining data (information) integrity across noisy channels and less than reliable storage… …   Wikipedia eye, human — ▪ anatomy Introduction  specialized sense organ capable of receiving visual images, which are then carried to the brain. Anatomy of the visual apparatus Structures auxiliary to the eye The orbit       The eye is protected from mechanical injury… …   Universalium 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”