Finite fields
Quantum computation and quantum information
Quantum computation and quantum information
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Asymmetric quantum codes: characterization and constructions
IEEE Transactions on Information Theory
New families of asymmetric quantum BCH codes
Quantum Information & Computation
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
Enlargement of Calderbank-Shor-Steane quantum codes
IEEE Transactions on Information Theory
Some good quantum error-correcting codes from algebraic-geometric codes
IEEE Transactions on Information Theory
Nonbinary quantum stabilizer codes
IEEE Transactions on Information Theory
Lower bounds on the quantum capacity and highest error exponent of general memoryless channels
IEEE Transactions on Information Theory
Quantum codes from concatenated algebraic-geometric codes
IEEE Transactions on Information Theory
Nonbinary Stabilizer Codes Over Finite Fields
IEEE Transactions on Information Theory
On Quantum and Classical BCH Codes
IEEE Transactions on Information Theory
Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Asymmetric quantum codes: new codes from old
Quantum Information Processing
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Two new families of asymmetric quantum codes are constructed in this paper. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to classical Reed-Solomon (RS) codes, providing quantum codes with parameters [[N = l(q l 驴1), K = l(q l 驴2d + c + 1), d z 驴 d/d x 驴 (d驴c)]] q , where q is a prime power and d c + 1, c 驴 1, l 驴 1 are integers. The second family is derived from the CSS construction applied to classical generalized RS codes, generating quantum codes with parameters [[N = mn, K = m(2k驴n + c), d z 驴 d/d x 驴 (d驴c)]] q , where q is a prime power, 1 k n k + c 驴 q m , k = n 驴 d + 1, and n, d c + 1, c 驴 1, m 驴 1 are integers. Although the second proposed construction generalizes the first one, the techniques developed in both constructions are slightly different. These new codes have parameters better than or comparable to the ones available in the literature. Additionally, the proposed codes can be utilized in quantum channels having great asymmetry, that is, quantum channels in which the probability of occurrence of phase-shift errors is large when compared to the probability of occurrence of qudit-flip errors.