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Quantum error correction via codes over GF(4)

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4 Author(s)
Calderbank, A.R. ; AT&T Labs.-Res., Florham Park, NJ, USA ; Rains, E.M. ; Shor, P.W. ; Sloane, N.J.A.

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

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 4 )