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{\bf Luis Goddyn and Pavol Gvozdjak  }
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{\bf Binary Gray Codes with Long Bit Runs}
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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.


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