Covering Radius and Packing Radius
For an code C (a subset of ), the covering radius of C is the smallest value of r such that every element of is contained in at least one ball of radius r centered at each codeword of C. The packing radius of C is the largest value of s such that the set of balls of radius s centered at each codeword of C are mutually disjoint.
From the proof of the Hamming bound, it can be seen that for, we have:
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- s ≤ t and t ≤ r.
Therefore, s ≤ r and if equality holds then s = r = t. The case of equality means that the Hamming bound is attained.
Read more about this topic: Hamming Bound
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