Use in Coding Theory
In the theory of Error-correcting codes, the metric space containing a block code C consists of strings of a fixed length, say n, taken over an alphabet of size q (can be thought of as vectors), with the Hamming metric. This space is denoted by . The covering radius of the code C is the smallest value of r > 0 such that the union of the spheres of radius r centered at the points of C (the codewords) is the entire space . This value is related to the code's ability to correct errors.
Read more about this topic: Covering Radius
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“No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
—André Gide (1869–1951)