Balancing Cyclic $R$-ary Gray Codes

Balancing Cyclic $R$-ary Gray Codes

New cyclic $n$-digit Gray codes are constructed over $\{0, 1, \ldots, R-1 \}$ for all $R \ge 3$, $n \ge 2$. These codes have the property that the distribution of the digit changes (transition counts) is close to uniform: For each $n \ge 2$, every transition count is within $R-1$ of the average $R^n...

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Veröffentlicht in:The Electronic journal of combinatorics 2007-04, Vol.14 (1)
Hauptverfasser: Flahive, Mary, Bose, Bella
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description New cyclic $n$-digit Gray codes are constructed over $\{0, 1, \ldots, R-1 \}$ for all $R \ge 3$, $n \ge 2$. These codes have the property that the distribution of the digit changes (transition counts) is close to uniform: For each $n \ge 2$, every transition count is within $R-1$ of the average $R^n/n$, and for the $2$-digit codes every transition count is either $\lfloor{R^2/2} \rfloor$ or $\lceil{R^2/2} \rceil$.
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