On perfect codes that do not contain Preparata-like codes
We show that for every length of form $4^k-1$, there exists a binary $1$-perfect code that does not include any Preparata-like code.
cs.IT↗
arXiv subjects
Anastasia Yu. Vasil'eva
Publications and source records attributed to Anastasia Yu. Vasil'eva.
On completely regular codes of covering radius 1 in the halved hypercubes
We consider constructions of covering-radius-1 completely regular codes, or, equivalently, equitable 2-partitions (regular 2-partitions, perfect 2-colorings), of halved n-cubes. Keywords: completely regular code, equitable partition, regular partition, partition design, perfect coloring, halved hypercube.
math.CO↗
Completely regular codes in the infinite hexagonal grid
A set $C$ of vertices of a simple graph is called a completely regular code if for each $i=0$, $1$, $2$, \ldots and $j = i-1$, $i$, $i+1$, all vertices at distance $i$ from $C$ have the same number $s_{ij}$ of neighbors at distance $j$ from $C$. We characterize the completely regular codes in the infinite hexagonal grid graph.
math.MG↗