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:
“We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
—Selma H. Fraiberg (20th century)
“He had a wonderful talent for packing thought close, and rendering it portable.”
—Thomas Babington Macaulay (1800–1859)