Quantum Error Correction and Orthogonal Geometry
  A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors. 
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 Defens...