On combinatorial Gray codes with distance 3. (English. Russian original) Zbl 1243.94045
Discrete Math. Appl. 19, No. 4, 383-388 (2009); translation from Diskretn. Mat. 21, No. 3, 73-78 (2009).
Summary: 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 construction method for Hamiltonian cycles in the graphs of minimum distances of binary Hamming codes. For all admissible lengths \(n \geq 15\), we give nonlinear perfect binary codes whose graphs of minimum distances contain a Hamiltonian cycle.
Keywords:
binary codes; cyclic codes; combinatorial codes; Gray codes; Hamming codes; perfect codes; Hamiltonian cycles; graphs of minimum distancesReferences:
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