Covering codes with improved density

Michael Krivelevich, Benny Sudakov, Van H. Vu

Research output: Contribution to journalLetterpeer-review

Abstract

We prove a general recursive inequality concerning μ* (R), the asymptotic (least) density of the best binary covering codes of radius R. In particular, this inequality implies that μ* (R) ≤ e · (R log R + log R + log log R + 2), which significantly improves the best known density 2R RR (R + 1) / R!. Our inequality also holds for covering codes over arbitrary alphabets.

Original languageEnglish
Pages (from-to)1812-1815
Number of pages4
JournalIEEE Transactions on Information Theory
Volume49
Issue number7
DOIs
StatePublished - Jul 2003

Keywords

  • Covering codes
  • Density
  • Probabilistic methods

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