An upper bound associated with errors in Gray code (Corresp.)

Abstract

Suppose <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0 \leq i,j \leq 2^n - 1</tex> . We prove that, if <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</tex> are encoded as binary Gray codewords whose Hamming distance is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m \geq 1</tex> , then <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mid i-j \mid &lt; 2^n - 2^m /3</tex> .