A Gray code of size n is a cyclic sequence of all binary words of length n such that two consecutive words differ exactly in one position. We say that the Gray code is a distance code if the Hamming distance between words located at distance k from each other is equal to d. The distance property generalizes the familiar concepts of a locally balanced Gray code. We prove that there are no distance Gray codes with d = 1 for k > 1. Some examples of constructing distance Gray codes are given. For one infinite series of parameters, it is proved that there are no distance Gray codes.

Original languageEnglish
Pages (from-to)185-192
Number of pages8
JournalJournal of Applied and Industrial Mathematics
Issue number2
Publication statusPublished - 1 Apr 2017


  • antipodal Gray code
  • Gray code
  • Hamiltonian cycle
  • n-cube
  • uniform Gray code


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