Covering radius
Encyclopedia
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
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of
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Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, 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
Linear code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although Turbo codes can be seen as a hybrid of these two types. Linear codes allow for...
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Example
In the real plane, the set of all integer points (i, j) has a covering radiusof
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