Probabilities of Failure for Quantum Error Correction
Quantum Information Processing
Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound
Quantum Information Processing
Cyclic Additive and Quantum Stabilizer Codes
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
On circulant self-dual codes over small fields
Designs, Codes and Cryptography
A family of asymptotically good quantum codes based on code concatenation
IEEE Transactions on Information Theory
Generalized concatenation for quantum codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Cyclic double struck capital Fq-linear double struck capital Fqt-codes
International Journal of Information and Coding Theory
On a problem concerning the quantum hamming bound for impure quantum codes
IEEE Transactions on Information Theory
Application of classical hermitian self-orthogonal MDS codes to quantum MDS codes
IEEE Transactions on Information Theory
Stabilizer codes can be realized as graph codes
Quantum Information & Computation
Homological invariants of stabilizer states
Quantum Information & Computation
Nonbinary quantum codes from hermitian curves
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Quantum codes from codes over Gaussian integers with respect to the Mannheim metric
Quantum Information & Computation
Hermitian dual containing BCH codes and construction of new quantum codes
Quantum Information & Computation
Asymmetric quantum codes: new codes from old
Quantum Information Processing
Quantum Information Processing
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We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than two states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional global symmetries. From this standpoint, the analogs of Calderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special cases of the same construction. This allows us to construct families of quantum codes from certain codes over number fields; in particular, we get analogs of quadratic residue codes, including a single-error-correcting code encoding one letter in five, for any alphabet size. We also consider the problem of fault-tolerant computation through such codes, generalizing ideas of Gottesman (see Phys. Rev. A, vol.57, no.1, p127-37, 1998)