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Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ${(0,1)}^n$ that differ from C in at most r of n position, S(C,r) for n=2k+1  

  1. For C,C’ $\epsilon$ ${(0,1)}^n$ S(C,k) and S(C’,k) are disjoint

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