Geodesic
On distance Gray codes
Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 2, pp. 5-17

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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. Tab. 5, bibliogr. 9.
Keywords: $n$-cube, Hamiltonian cycle, Gray code, uniform Gray code
Mots-clés : antipodal Gray code. 
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     author = {I. S. Bykov and A. L. Perezhogin},
     title = {On distance {Gray} codes},
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I. S. Bykov; A. L. Perezhogin. On distance Gray codes. Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 2, pp. 5-17. http://geodesic.mathdoc.fr/item/DA_2017_24_2_a0/