Title :
The multicovering radii of codes
Author_Institution :
Dept. of Comput. Sci., Kentucky Univ., Lexington, KY, USA
fDate :
7/1/1997 12:00:00 AM
Abstract :
The covering radius of a code is the least r such that the set of balls of radius r around codewords covers the entire ambient space. We introduce a generalization of the notion of covering radius. The m-covering radius of a code is the least radius such that the set of balls of that radius covers all m-tuples of elements in the ambient space. We investigate basic properties of m-covering radii. We investigate whether codes exist with given m-covering radii (not always). We derive bounds on the size of the smallest code with a given m-covering radius, based on generalizations of the sphere bound and the method of counting excesses
Keywords :
Hamming codes; binary sequences; block codes; Hamming codes; ambient space; binary codes; covering radius; lower bound; m-covering radius; method of counting excesses; multicovering radii; sphere bound; Associate members; Binary codes; Binary sequences; Block codes; Communication system control; Computer science; Resists;
Journal_Title :
Information Theory, IEEE Transactions on
