Antipodal Gray codes
In a private e-mail communication, Snevily (2000) found \(n\)-bit antipodal Gray codes for \(n= 1,2,3,4\) and posed a problem whether they exist for larger \(n\). This paper gives a partial answer to this question. It is proved that for odd \(n> 3\), an \(n\)-bit antipodal Gray code is not possible. The authors made an exhaustive computer search showing that there exists no 6-bit antipodal Gray code. However, it is shown that when \(n\) is power of 2, \(n\)-bit antipodal Gray codes do exist, and the authors provide a recursive construction. The paper concludes with some remaining open cases.
scientific article; zbMATH DE number 2083671