Diskretnaya Matematika, Tome 21 (2009) no. 3, pp. 73-78
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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/
@article{DM_2009_21_3_a6,
author = {A. M. Romanov},
title = {On combinatorial {Gray} codes with distance~3},
journal = {Diskretnaya Matematika},
pages = {73--78},
year = {2009},
volume = {21},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2009_21_3_a6/}
}
TY - JOUR
AU - A. M. Romanov
TI - On combinatorial Gray codes with distance 3
JO - Diskretnaya Matematika
PY - 2009
SP - 73
EP - 78
VL - 21
IS - 3
UR - http://geodesic.mathdoc.fr/item/DM_2009_21_3_a6/
LA - ru
ID - DM_2009_21_3_a6
ER -
%0 Journal Article
%A A. M. Romanov
%T On combinatorial Gray codes with distance 3
%J Diskretnaya Matematika
%D 2009
%P 73-78
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/DM_2009_21_3_a6/
%G ru
%F DM_2009_21_3_a6
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.
