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pro vyhledávání: '"Vasil'eva, Anastasia Yu."'
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 partitio
Externí odkaz:
http://arxiv.org/abs/1812.03159
Publikováno v:
Sib. Elektron. Mat. Izv. (Siberian Electronic Mathematical Reports) 13, 2016, 987-1016
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 c
Externí odkaz:
http://arxiv.org/abs/1612.01360
Publikováno v:
Probl. Inf. Transm. 52(3) 2016, 284-288 (English); Probl. Peredachi Inf. 52(3) 2016, 92-96 (Russian)
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.
Comment: Eng. 4pp + Rus. 5pp. v.2: English translation added. v.3: accepted version (minor revision, more explan
Comment: Eng. 4pp + Rus. 5pp. v.2: English translation added. v.3: accepted version (minor revision, more explan
Externí odkaz:
http://arxiv.org/abs/1512.03048