  In this paper, we prove how to extend a subset of quantum stabilizer codes
into a qudit hybrid code storing $\log_2 p$ classical bits over a qudit space
with dimension $p$, with $p$ prime. Our proof also gives an explicit procedure
for finding the entire collection of stabilizer algebras for all of the
subcodes of the hybrid code. This allows extra classical information to be
transmitted without having to arduously search for additional codes and their
associated codewords, and also provides a first lower bound to the amount of
classical information able to be transmitted in a qudit hybrid code, but
unfortunately only allows for $\log_2 p$ classical bits to be decoded by a
receiver.
