Quantum Error Correction via Codes over GF(4)
  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. 
A. R. Calderbank (1), E. M Rains (2), P. W. Shor (1), and N. J. A.   Sloane (1), ((1) AT&T Research, (2) Institute for Defen...