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Zbl 0982.94029
Calderbank, A.Robert; Rains, Eric M.; Shor, P.W.; Sloane, Neil J.A.
Quantum error correction via codes over $\mathrm{GF}(4)$.
(English)
[J] IEEE Trans. Inf. Theory 44, No.4, 1369-1387 (1998). ISSN 0018-9448

Summary: The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) that 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.
MSC 2000:
*94B60 Other types of codes
81P68 Quantum computation and quantum cryptography

Keywords: quaternary codes; symplectic group; quantum error-correcting codes; additive codes; self-orthogonal

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