1 citations · 1 across the 5 of their papers we have counts for
6 papers
On completely regular codes of covering radius 1 in the halved hypercubes
Denis S. Krotov, Ivan Yu. Mogilnykh, Anastasia Yu. Vasil'eva
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. Ke…
Completely regular codes in the infinite hexagonal grid
Sergey V. Avgustinovich, Denis S. Krotov, Anastasia Yu. Vasil'eva
A set of vertices of a simple graph is called a completely regular code if for each , , , \ldots and , , , all vertices at distance from hav…
On perfect codes that do not contain Preparata-like codes
Denis S. Krotov, Anastasia Yu. Vasil'eva
We show that for every length of form , there exists a binary -perfect code that does not include any Preparata-like code.
Distance Regular Colorings of -Dimensional Rectangular Grid
Sergey Avgustinovich, Anastasia Vasil'eva
We study the infinite graph of -dimensional rectangular grid that doesn't appear distance regular and the distance regular colorings of this graph, which are defined as the dist…
Local distributions for eigenfunctions and for perfect colorings of q-ary hypercube
Anastasia Vasil'eva
Under study are the eigenfunctions and perfect colorings of the graph of -dimensional -ary Hamming space. We obtain the interdependence of local distributions of an eigenfunc…
Reconstruction of Eigenfunctions of q-ary n-dimensional Hypercube
Anastasia Vasil'eva
Under study are eigenfunctions of -ary -dimensional hypercube. Given all values of an eigenfunction in the sphere we develop methods to reconstruct the function in full or in…