Geodesic
Binary Gray codes with long bit runs
The electronic journal of combinatorics, Tome 10 (2003)
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We show that there exists an $n$-bit cyclic binary Gray code all of whose bit runs have length at least $n - 3\log_2 n$. That is, there exists a cyclic ordering of $\{0,1\}^n$ such that adjacent words differ in exactly one (coordinate) bit, and such that no bit changes its value twice in any subsequence of $n-3\log_2 n$ consecutive words. Such Gray codes are 'locally distance preserving' in that Hamming distance equals index separation for nearby words in the sequence.
DOI : 10.37236/1720
Classification : 05C38, 05C45, 68R15
Mots-clés : Hamilton cycle, Hamilton circle, spread, gap, threshold, Hamming distance 
@article{10_37236_1720,
     author = {Luis Goddyn and Pavol Gvozdjak},
     title = {Binary {Gray} codes with long bit runs},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1720},
     zbl = {1023.05080},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1720/}
}
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%A Pavol Gvozdjak
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Luis Goddyn; Pavol Gvozdjak. Binary Gray codes with long bit runs. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1720

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