Covering codes with improved density

We prove a general recursive inequality concerning /spl mu//sup */(R), the asymptotic (least) density of the best binary covering codes of radius R. In particular, this inequality implies that /spl mu//sup */(R)/spl les/e/spl middot/(RlogR+logR+loglogR+2), which significantly improves the best known...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 49; no. 7; pp. 1812 - 1815
Main Authors Krivelevich, M., Sudakov, B., Vu, V.H.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2003
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Alphabets
Asymptotic properties
Codes
Covering
Density
Error correction codes
Hamming distance
Hypercubes
Inequalities
Information systems
Information theory
Mathematics
Recursive
Upper bound
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Summary:We prove a general recursive inequality concerning /spl mu//sup */(R), the asymptotic (least) density of the best binary covering codes of radius R. In particular, this inequality implies that /spl mu//sup */(R)/spl les/e/spl middot/(RlogR+logR+loglogR+2), which significantly improves the best known density 2/sup R/R/sup R/(R+1)/R!. Our inequality also holds for covering codes over arbitrary alphabets.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.813490