KIAM Main page Web Library  •  Publication Searh  Русский 

Article collection "Mathematical Problems of Cybernetics" №20, Moscow, 2022
Authors: Perezhogin A.L., Bykov I.S.
Overview of constructions and properties of Gray codes
Cyclic enumeration of binary words of length n, where each pair of adjacent words differs in exactly one index, is called n-dimensional Gray code. Gray code determines hamiltonian cycle in boolean n-cube. In this paper we give a review of constructions and classifications of Gray codes. Constructions are divided into three main groups: recursive, toric and stream. We also give some of Gray code properties, as an example of applications of these constructions. In particular, we consider spectrum of edge directions, graphs of 2-subwords in transition sequence, local uniformity and others. Also some unresolved problems are given.
Gray code, hamiltonian cycle, boolean cube, transition sequence
Publication language: russian,  pages: 20 (p. 41-60)
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
Export link to publication in format:   RIS    BibTeX
About authors:
  • Perezhogin Aleksey Lvovich, Institute of Mathematics
  • Bykov Igor Sergeevich, State University