DocumentCode
893389
Title
Inequalities for covering codes
Author
Calderbank, A.R. ; Sloane, N. J A
Author_Institution
AT&T Bell Lab., Murray Hill, NJ, USA
Volume
34
Issue
5
fYear
1988
fDate
9/1/1988 12:00:00 AM
Firstpage
1276
Lastpage
1280
Abstract
Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial L R(x ); these generalize the sphere bound. Syndrome graphs associated with a linear code C are introduced to help keep track of low-weight vectors in the same coset of C (if there are too many such vectors C cannot exist). Illustrations show that t [17, 10]=3 and t [23, 15]=3 where t [n , k ] is the smallest covering radius of any [n , k ] code
Keywords
boundary-value problems; codes; encoding; polynomials; Lloyd polynomial; coset; covering codes; covering radius; linear code; linear inequalities; low-weight vectors; sphere bound; syndrome graph; Algebra; Binary codes; Error correction codes; Helium; Linear code; Linear programming; Polynomials; Vectors;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.21257
Filename
21257
Link To Document