DocumentCode
1256788
Title
Linear inequalities for covering codes. I. Pair covering inequalities
Author
Zhang, Zhen
Author_Institution
Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA
Volume
37
Issue
3
fYear
1991
fDate
5/1/1991 12:00:00 AM
Firstpage
573
Lastpage
582
Abstract
The lower bounds on K(n,R), minimum number of codewords of any binary code of length n, and covering radius R are improved. A new technique combining the Hamming association scheme and the results of a classic problem of covering pairs by k-tuples is introduced. The new lower bounds are obtained by studying various linear inequalities satisfied by covering codes, and such an inequality is derived. The lower bounds for K(n,R) are studied for some special values of n and R, which serve as examples showing how the methods developed are applied to concrete cases.
Keywords
error correction codes; Hamming association scheme; binary code; covering codes; covering pairs; covering radius; k-tuples; linear inequalities; lower bounds; minimum number of codewords; pair covering inequalities; Binary codes; Concrete; Error correction codes; History; Linear code; Technological innovation; Upper bound;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.79914
Filename
79914
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