\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Mary Flahive }
%
%
\medskip
\noindent
%
%
{\bf Balancing Cyclic $R$-ary Gray Codes$\,$ II}
%
%
\vskip 5mm
\noindent
%
%
%
%
New cyclic $n$-digit Gray codes are constructed over {$\{0, 1, \ldots,
R-1 \}$} for all {$R \ge 2$, $n \ge 3$.}  These codes have the
property that the distribution of digit changes (transition counts)
between two successive elements is close to uniform.  For $R=2$, the
construction and proof are simpler than earlier balanced cyclic binary
Gray codes.  For $R \ge 3$ and {$n \ge 2$,} every transition count is
within $2$ of the average~$R^n/n$.  For even~$R >2$, the codes are as
close to uniform as possible, except when there are two anomalous
transition counts for $R \equiv 2 \pmod{4}$ and $R^n$ is divisible by $n$.





\bye

.