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On combinatorial Gray codes with distance 3
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A. M. Romanov
Published/Copyright:
October 19, 2009
Abstract
We suggest a construction of the cyclic binary combinatorial Gray codes with distance 3 and dimension n = 2k – 1, where k = 3, 4, . . . We give a method of construction of Hamiltonian cycles in the graphs of minimum distances of binary Hamming codes. For all admissible lengths n ≥ 15, we give nonlinear perfect binary codes whose graphs of minimum distances contain a Hamiltonian cycle.
Received: 2008-05-05
Revised: 2009-05-05
Published Online: 2009-10-19
Published in Print: 2009-October
© de Gruyter 2009
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