On mixed codes with covering radius 1 and minimum distance 2
The electronic journal of combinatorics, Tome 14 (2007)
Let $R$, $S$ and $T$ be finite sets with $|R|=r$, $|S|=s$ and $|T|=t$. A code $C\subset R\times S\times T$ with covering radius $1$ and minimum distance $2$ is closely connected to a certain generalized partial Latin rectangle. We present various constructions of such codes and some lower bounds on their minimal cardinality $K(r,s,t;2)$. These bounds turn out to be best possible in many instances. Focussing on the special case $t=s$ we determine $K(r,s,s;2)$ when $r$ divides $s$, when $r=s-1$, when $s$ is large, relative to $r$, when $r$ is large, relative to $s$, as well as $K(3r,2r,2r;2)$. Some open problems are posed. Finally, a table with bounds on $K(r,s,s;2)$ is given.
@article{10_37236_969,
author = {Wolfgang Haas and J\"orn Quistorff},
title = {On mixed codes with covering radius 1 and minimum distance 2},
journal = {The electronic journal of combinatorics},
year = {2007},
volume = {14},
doi = {10.37236/969},
zbl = {1160.94019},
url = {http://geodesic.mathdoc.fr/articles/10.37236/969/}
}
Wolfgang Haas; Jörn Quistorff. On mixed codes with covering radius 1 and minimum distance 2. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/969
Cité par Sources :