Completely regular codes in the $n$-Dimensional Rectangular Grid
Ключевые слова:
n-dimensional rectangular grid, completely regular code, intersection array, covering radius, perfect coloringАннотация
It is proved that two sequences of the intersection array
of an arbitrary completely regular code in
the $n$-dimensional rectangular grid are monotonic.
It is shown that the minimal distance of an arbitrary
completely regular code is at most 4 and the covering radius
of an irreducible completely regular code in the grid
is at most $2n$.
Опубликован
2023-08-03
Выпуск
Раздел
ДИСКРЕТНАЯ МАТЕМАТИКА И МАТЕМАТИЧЕСКАЯ КИБЕРНЕТИКА