  Encoding readout methods based on different schemes have been successfully
developed and tested with different types of position-sensitive detectors with
strip-readout structures. However, how to construct an encoding scheme in a
more general and systematic way is still under study. In this paper, we present
a graph model for the encoding scheme. With this model, encoding schemes can be
studied in a more systematic way. It is shown that by using an encoding readout
method, a maximum of n(n-1)/2+1 strips can be processed with n channels if n is
odd, while a maximum of (n(n-2))/2+2 strips can be processed with n channels if
n is even. Furthermore, based on the model, the encoding scheme construction
problem can be translated into a problem in graph theory, the aim of which is
to construct an Eulerian trail such that the length of the shortest subcycle is
as long as possible. A more general approach to constructing the encoding
scheme is found by solving the associated mathematical problem. In addition, an
encoding scheme prototype has been constructed, and verified with MRPC
detectors.
