A deterministic $ (2−2/(k+1))^n$ algorithm for $ k$ -SAT based on local search
I have read this paper and I couldn’t understand how to culculate the $ covering$ $ radius$ of a code in the Hamming space. It is defined as follows in the paper.
We identify assignments with binary words. The set of these words of length $ n$ is the $ Hamming$ $ space$ denoted by $ H_n=\{0,1\}^n$ . The $ Hamming$ $ distance$ between two assignments is the number of positions in which these two assignments differ. The $ ball$ of radius $ r$ around an assignment $ a$ is the set of all assignments whose Hamming distance to $ a$ is at most $ r$ .
A $ code$ of length $ n$ is simply a subset of $ H_n$ . The $ covering$ $ radius$ $ r$ of a code $ C$ is defined by $ $ r=\max_{u∈\{0,1\}^n}\min_{v∈C }d(u,v),$ $ where $ d(u,v)$ denotes the Hamming distance between $ u$ and $ v$ .
The $ \max$ of $ \min$ is exactly the point I couldn’t calculate. So I considered the instance of $ C$ and tried to calculate its covering radius.
e.g.)$ $ C=\{000,010,011,100,101,110\}⊆H_3$ $ 
In this case, how can I calculate the covering radius $ r$ ?
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