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Let <math>q\geq 2</math>, <math>n\geq 1</math>, <math>R\geq 0</math> be [[integers]].
A [[code]] <math>C\subseteq Q^n</math> over an [[alphabet]] ''Q'' of size |''Q''| = ''q'' is called
''q''-ary R-'''covering code''' of length ''n''
if for every word <math>y\in Q^n</math> there is a [[codeword]] <math>x\in C</math>
such that the [[Hamming distance]] <math>d_H(x,y)\leq R</math>.
In other words, the [[spheres]] (or [[balls]] or [[rook]]-domains) of [[radius]] ''R''
with respect to the Hamming [[metric]] around the codewords of ''C'' have to exhaust
the [[finite]] [[metric space]] <math>Q^n</math>.
Every [[perfect code]] is a covering code of minimal size.
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