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:
-
- 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
Famous quotes containing the words covering and/or packing:
“You had to have seen the corpses lying there in front of the school—the men with their caps covering their faces—to know the meaning of class hatred and the spirit of revenge.”
—Alfred Döblin (1878–1957)
“He had a wonderful talent for packing thought close, and rendering it portable.”
—Thomas Babington Macaulay (1800–1859)