Nonbinary quantum stabilizer codes

From MaRDI portal
Publication:4544755

DOI10.1109/18.959288zbMath1021.94033arXivquant-ph/0005008OpenAlexW2143438504MaRDI QIDQ4544755

Emanuel Knill, Alexei Ashikhmin

Publication date: 4 August 2002

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0005008




Related Items

Galois quantum systems, irreducible polynomials and Riemann surfacesNEW QUANTUM CODES CONSTRUCTED FROM A CLASS OF IMPRIMITIVE BCH CODESOn non-binary quantum repeated-root cyclic codesEntanglement-assisted quantum codes constructed from primitive quaternary BCH codesOn the construction of optimal asymmetric quantum codesUnnamed ItemA lower bound on the quantum capacity of channels with correlated errorsLower bound for the quantum capacity of a discrete memoryless quantum channelQuantum error-correcting codes from the quantum construction \(X\)Quantum codes from a new construction of self-orthogonal algebraic geometry codesQuantum codes from codes over the ring \(\mathbb{F}_q + \alpha\mathbb{F}_q\)Classical access structures of ramp secret sharing based on quantum stabilizer codesNew quantum MDS codes over finite fieldsNew EAQEC codes constructed from Galois LCD codesSome negacyclic BCH codes and quantum codesA class of constacyclic codes are generalized Reed-Solomon codesNon-binary entanglement-assisted stabilizer codesQuantum MDS codes with new length and large minimum distanceQuantum MDS and synchronizable codes from cyclic codes of length \(5p^s\) over \(\mathbb{F}_{p^m}\)Two classes of quantum codes from almost MDS codesImproved construction of quantum constacyclic BCH codes\((x^n - (a+bw), \xi, \eta)\)-skew constacyclic codes over \(\mathbb{F}_q + w\mathbb{F}_q\) and their applications in quantum codesSteane enlargement of entanglement-assisted quantum error-correcting codesConstruction of quantum MDS codes from generalized Reed–Solomon codesNew entanglement-assisted quantum MDS codes with length \(n = \frac{q^2+1}{5}\)The images of constacyclic codes and new quantum codesNew quantum codes from matrix-product codes over small fieldsQuantum bicyclic hyperbolic codesA new construction of quantum codes from quasi-cyclic codes over finite fieldsOptimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length \(3p^s\)New quantum codes derived from group ringsTwo new classes of Hermitian self-orthogonal non-GRS MDS codes and their applicationsSome new quantum MDS codes derived from generalized Reed-Solomon codesSymplectic isometries of stabilizer codesConstruction and enumeration of self-orthogonal and self-dual codes over Galois rings of even characteristicConstructions of quantum MDS codesConstruction of new quantum codes via Hermitian dual-containing matrix-product codesSeveral classes of Galois self-orthogonal MDS codes and related applicationsQuantum codes from trace codesSome quantum synchronizable codes with explicit distanceSome new quantum codes from constacyclic codesNew quantum codes from the images of cyclic codesMinimal and optimal binary codes obtained using \(C_D\)-construction over the non-unital ring \(I\)Theory behind quantum error correcting codes: an overviewNew quantum stabilizer codes with better parameters from the images of some RS codes and BCH codesLocal-dimension-invariant Calderbank-Shor-Steane codes with an improved distance promiseFault-tolerant error correction for quantum Hamming codes with only two ancillary quditsSome new constructions of optimal asymmetric quantum codesQuantum and LCD codes from skew constacyclic codes over a finite non-chain ringApplication of Euclidean sums of matrix-product codes to quantum codesHermitian dual-containing constacyclic codes over \(\mathbb{F}_{q^2}+v_1 \mathbb{F}_{q^2}+\cdots +v_r \mathbb{F}_{q^2}\) and new quantum codesThree classes of new EAQEC MDS codesQuantum codes from Hermitian dual-containing constacyclic codes over \(\mathbb{F}_{q^2} + v\mathbb{F}_{q^2}\)EAQEC codes from two distinct constacyclic codesQuantum memories and error correctionPractical demonstration of quantum key distribution protocol with error correction mechanismA class of Hermitian dual-containing constacyclic codes and related quantum codesConstructing quantum error-correcting codes that require a variable amount of entanglementStabilizer quantum codes defined by trace-depending polynomialsNew binary quantum codes from group rings and skew group ringsNew quantum codes derived from a family of antiprimitive BCH codesA family of Hermitian dual-containing constacyclic codes and related quantum codesEntanglement-assisted Reed-Solomon codes over qudits: theory and architectureNarain CFTs from nonbinary stabilizer codesStabilizer codes and equientangled bases from phase statesConstruction of new quantum MDS codes derived from constacyclic codesOne-generator quasi-cyclic codes and their dual codesGalois hulls of special Goppa codes and related codes with application to EAQECCsNew optimal asymmetric quantum codes constructed from constacyclic codesConstruction of quantum negacyclic BCH codesClassic and Quantum Error Correcting CodesIdentification of a reversible quantum gate: assessing the resourcesSome families of optimal quantum codes derived from constacyclic codesNew quantum codes from Hermitian dual-containing codesVariations on Encoding Circuits for Stabilizer Quantum CodesUnnamed ItemON OPTIMAL QUANTUM CODESA new construction of quantum error-correcting codesQuantum codes from Hadamard matricesStandard form of qudit stabilizer groupsTwo families of BCH codes and new quantum codesTwo families of BCH codes and new quantum codesFully Ramified Characters and Clifford CodesTERNARY QUANTUM CODES OF MINIMUM DISTANCE THREENew quantum constacyclic codes with length n=2(qm+1)Noisy Interactive Quantum CommunicationStabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmeticDiscrete phase space based on finite fieldsON THE AUTOMORPHISM GROUPS OF A FAMILY OF BINARY QUANTUM ERROR-CORRECTING CODESNonbinary quantum codesUnnamed ItemNew quantum MDS codesAsymmetric quantum convolutional codesQuasi-cyclic constructions of asymmetric quantum error-correcting codesConstruction of some new quantum MDS codesA construction of optimal nonbinary pure quantum stabilizer codesNew constructions of entanglement-assisted quantum codesOn the generalization of the construction of quantum codes from Hermitian self-orthogonal codesNew entanglement-assisted quantum codes from \(k\)-Galois dual codesOn some binary symplectic self-orthogonal codesQuantum codes from cyclic codes over the ring \(\mathbb{F}_q+v_1\mathbb{F}_q+\cdots +v_r\mathbb{F}_q\)Quasi-cyclic constructions of quantum codesThe Frobenius formalism in Galois quantum systemsNonbinary quantum Goppa codes exceeding the quantum Gilbert-Varshamov boundNew \(q\)-ary quantum MDS codes with distances bigger than \(\frac{q}{2}\)Quantum error-correcting codes from algebraic geometry codes of castle typeA study of quantum codes obtained from cyclic codes over a non-chain ringTwo new classes of quantum MDS codesConstacyclic codes over finite commutative semi-simple ringsTernary self-orthogonal codes of dual distance three and ternary quantum codes of distance threeOn the construction of quantum constacyclic codesSome quantum MDS codes with large minimum distance from generalized Reed-Solomon codesA class of negacyclic BCH codes and its application to quantum codesQuantum MDS codes with relatively large minimum distance from Hermitian self-orthogonal codesA family of negacyclic BCH codes of length \(n=\frac{q^{2m}-1}{2} \)Constructions of optimal Hermitian self-dual codes from unitary matricesA class of constacyclic BCH codes and new quantum codesOn the distance of stabilizer quantum codes from \(J\)-affine variety codesA different construction for some classes of quantum MDS codesNew quantum codes from two linear codesNonbinary quantum codes from constacyclic codes over polynomial residue ringsNew EAQEC codes from cyclic codes over \(\mathbb{F}_q + u\mathbb{F}_q\)Entanglement-assisted quantum codes from cyclic codes and negacyclic codesNew quantum MDS codes with large minimum distance and short length from generalized Reed-Solomon codesOn quantum stabilizer codes derived from local Frobenius ringsOn cyclotomic cosets and code constructionsTwo Gilbert-Varshamov-type existential bounds for asymmetric quantum error-correcting codesAsymmetric quantum Reed-Solomon and generalized Reed-Solomon codesUnitary reconstruction of secret for stabilizer-based quantum secret sharingMessage randomization and strong security in quantum stabilizer-based secret sharing for classical secretsCodes as fractals and noncommutative spacesOn new quantum codes from matrix product codesAsymmetric quantum codes: new codes from oldMDS constacyclic codes of prime power lengths over finite fields and construction of quantum MDS codesOn negacyclic MDS-convolutional codesOn the construction of asymmetric quantum codesEuclidean and Hermitian self-dual MDS codes over large finite fields.Nonbinary quantum error-correcting codes from algebraic curvesWeight enumerators for nonbinary asymmetric quantum codes and their applicationsSelf-orthogonal codes with dual distance three and quantum codes with distance three over \(\mathbb F_5\)New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codesEntanglement-assisted quantum error-correcting codes over arbitrary finite fieldsOn the construction of quantum MDS codesQuantum codes and entanglement-assisted quantum codes derived from one-generator quasi-twisted codesQuantum codes from repeated-root cyclic and negacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m} \)Some new entanglement-assisted quantum error-correcting MDS codes with length \(\frac{q^2+1}{13} \)The asymptotic probability distribution of the relative distance of additive quantum codesNew quantum codes from dual-containing cyclic codes over finite ringsConstacyclic codes over the ring \(\mathbb {F}_q+v\mathbb {F}_q+v^2\mathbb {F}_q\) and their applications of constructing new non-binary quantum codesNew quantum MDS code from constacyclic codesQuantum MDS codes from BCH constacyclic codesQuantum MDS codes with large minimum distanceFundamentals of quantum information theoryPractical entanglement distillation scheme using recurrence method and quantum low density parity check codesProbabilities of failure for quantum error correctionConstructions of new families of nonbinary CSS codesNew quantum MDS codes derived from constacyclic codesSome families of asymmetric quantum MDS codes constructed from constacyclic codesQuantum codes derived from one-generator quasi-cyclic codes with Hermitian inner productStabilizer quantum codes from \(J\)-affine variety codes and a new Steane-like enlargementNew quantum codes from evaluation and matrix-product codesExtended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codesNew stabilizer codes from the construction of dual-containing matrix-product codesSome new quantum MDS codes from generalized Reed-Solomon codesLinear \(\ell\)-intersection pairs of MDS codes and their applications to AEAQECCsNew entanglement-assisted quantum MDS codes with length \(n=\frac{q^2+1}{10\mu }\)Three new classes of entanglement-assisted quantum MDS codes from cyclic codesNew constructions of optimal subsystem codesA new construction of linear codes with one-dimensional hullQuantum MDS and synchronizable codes from cyclic and negacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m}\)New quantum constacyclic codesEntanglement-assisted quantum codes from matrix-product codesFault-tolerant quantum computation with non-binary systemsTwo classes of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codesNew quantum codes derived from images of cyclic codesOn construction of quantum codes with dual-containing quasi-cyclic codesSome constructions of optimal subsystem codes derived from GRS codesSome entanglement-assisted quantum MDS codes with large minimum distanceLinear codes with arbitrary dimensional hull and their applications to EAQECCsQEC and EAQEC codes from cyclic codes over non-chain ringsConstacyclic codes over \(\mathbb{F}_{q^2}[u/\langle u^2-w^2 \rangle\) and their application in quantum code construction] ⋮ Hermitian dual-containing narrow-sense constacyclic BCH codes and quantum codesSome families of asymmetric quantum codes and quantum convolutional codes from constacyclic codesA novel qutrit representation of quantum imageA fast quantum image encryption algorithm based on affine transform and fractional-order Lorenz-like chaotic dynamical systemConstruction of new entanglement-assisted quantum MDS codes via cyclic codesConstructions of new nonbinary quantum codesEntanglement-assisted quantum error correction codes with length \(n=q^2+1\)Good rate QECCs from the quantum construction \(X\)New constructions of quantum MDS codes over finite fieldsSome new classes of quantum BCH codesQuantum codes from affine variety codes and their subfield-subcodes