Geodesic
On combinatorial Gray codes with distance~3
Diskretnaya Matematika, Tome 21 (2009) no. 3, pp. 73-78

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We suggest a construction of the cyclic binary combinatorial Gray codes with distance 3 and dimension $n=2^k-1$, where $k=3,4,\dots$. We give a method of construction of Hamiltonian cycles in the graphs of minimum distances of binary Hamming codes. For all admissible lengths $n\ge15$, we give nonlinear perfect binary codes whose graphs of minimum distances contain a Hamiltonian cycle. 
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     author = {A. M. Romanov},
     title = {On combinatorial {Gray} codes with distance~3},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2009_21_3_a6/}
}
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A. M. Romanov. On combinatorial Gray codes with distance~3. Diskretnaya Matematika, Tome 21 (2009) no. 3, pp. 73-78. http://geodesic.mathdoc.fr/item/DM_2009_21_3_a6/