Quantum Error Correction Via Codes Over

The problem of finding quantum-error-correcting codes is transformed into the problem of finding additive codes over the field GF (4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits. Manuscript received ; revised The authors are with AT&T Labs Research, Florham Park, NJ 07932-0971, USA. The work of the second author was performed while he was with the Institute for Defense Analyses, Princeton, NJ, USA.