\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 Joanne L. Hall}
%
%
\medskip
\noindent
%
%
{\bf Graphs Associated with Codes of Covering Radius 1 and Minimum Distance 2}
%
%
\vskip 5mm
\noindent
%
%
%
%
The search for codes of covering radius $1$ led \"{O}sterg{\aa}rd,
Quistorff and Wassermann to the OQW method of associating a unique
graph to each code.  We present results on the structure and existence
of OQW-associated graphs.  These are used to find an upper bound on
the size of a ball of radius $1$ around a code of length $3$ and
minimum distance $2$.  OQW-associated graphs and non-extendable
partial Latin squares are used to catalogue codes of length $3$ over
$4$ symbols with covering radius $1$ and minimum distance $2$.

\bye

.
