DocumentCode
1355943
Title
The multicovering radii of codes
Author
Klapper, Andrew
Author_Institution
Dept. of Comput. Sci., Kentucky Univ., Lexington, KY, USA
Volume
43
Issue
4
fYear
1997
fDate
7/1/1997 12:00:00 AM
Firstpage
1372
Lastpage
1377
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;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.605612
Filename
605612
Link To Document