Subsystem Codes

We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the question whether or not there exist [[n, n− 2d+2, r > 0, d]]q subsystem codes. Finally, we compare stabilizer and subsystem codes with respect to the required number of syndrome qudits.