Abstract
In this paper, we prove how to extend a subset of quantum stabilizer codes into a qudit hybrid code storing log₂ 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 log₂ p classical bits to be decoded by a receiver.