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Covering codes with improved density

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3 Author(s)
Krivelevich, M. ; Dept. of Math., Tel-Aviv Univ., Israel ; Sudakov, B. ; Vu, V.H.

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·(RlogR+logR+loglogR+2), which significantly improves the best known density 2RRR(R+1)/R!. Our inequality also holds for covering codes over arbitrary alphabets.

Published in:

Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 7 )