COMPLETELY REGULAR CODES IN THE n-DIMENSIONAL RECTANGULAR GRID
Keywords:
n-dimensional rectangular grid, completely regular code, intersection array, covering radius, perfect coloringAbstract
We study codes and colorings in the infinite graph of n-dimensional rectangular grid. The parameter matrix of the distance coloring with respect to an arbitrary completely regular codes is investigated. It is shown that the covering radius of an arbitrary completely regular code in the n-dimensional rectangular grid is at most 2n and the minimal distance is at most 4.
Published
2023-08-03
Issue
Section
Discrete mathematics and mathematical cybernetics