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Paper Title On two-fold packings of radius-1 balls in Hamming graphs
Paper IdentifierFR2.R9.1
Authors Denis S. Krotov, Vladimir N. Potapov, Sobolev Institute of Mathematics, Russia
Session Packings and Combinatorics
Location Pontoise, Level 5
Session Time Friday, 12 July, 11:40 - 13:00
Presentation Time Friday, 12 July, 11:40 - 12:00
Manuscript  Click here to download the manuscript
Abstract A $\lambda$-fold $r$-packing in a Hamming metric space is a code $C$ such that the radius-$r$ balls centered in $C$ cover each vertex of the space by not more than $\lambda$-times. The well-known $r$-error-correcting codes correspond to the case $\lambda=1$. We propose asymptotic bounds for $q$-ary $2$-fold $1$-packings as $q$ grows, find that the maximum size of a binary $2$-fold $1$-packing of length $9$ is $96$, and derive upper bounds for the size of a binary $\lambda$-fold $1$-packing.