TY - JOUR
T1 - Covering codes with improved density
AU - Krivelevich, Michael
AU - Sudakov, Benny
AU - Vu, Van H.
PY - 2003/7
Y1 - 2003/7
N2 - 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.
AB - 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.
KW - Covering codes
KW - Density
KW - Probabilistic methods
UR - http://www.scopus.com/inward/record.url?scp=0038782229&partnerID=8YFLogxK
U2 - 10.1109/TIT.2003.813490
DO - 10.1109/TIT.2003.813490
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AN - SCOPUS:0038782229
SN - 0018-9448
VL - 49
SP - 1812
EP - 1815
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 7
ER -