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.
|Number of pages||8|
|Journal||Journal of Applied and Industrial Mathematics|
|Publication status||Published - 1 Apr 2017|
- antipodal Gray code
- Gray code
- Hamiltonian cycle
- uniform Gray code