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Covering code : ウィキペディア英語版
Covering code
In coding theory, a covering code is a set of elements (called ''codewords'') in a space, with the property that every element of the space is within a fixed distance of some codeword.
== Definition ==

Let q\geq 2, n\geq 1, R\geq 0 be integers.
A code C\subseteq Q^n over an alphabet ''Q'' of size |''Q''| = ''q'' is called
''q''-ary ''R''-covering code of length ''n''
if for every word y\in Q^n there is a codeword x\in C
such that the Hamming distance d_H(x,y)\leq R.
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 Q^n.
The covering radius of a code ''C'' is the smallest ''R'' such that ''C'' is ''R''-covering.
Every perfect code is a covering code of minimal size.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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