Abstract
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 language | English |
|---|---|
| Pages (from-to) | 185-192 |
| Number of pages | 8 |
| Journal | Journal of Applied and Industrial Mathematics |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2017 |
Keywords
- antipodal Gray code
- Gray code
- Hamiltonian cycle
- n-cube
- uniform Gray code