Constructions of new entanglement-assisted quantum MDS and almost MDS codes

DOI10.1007/s11128-019-2197-6zbMath1417.81110OpenAlexW2911543128MaRDI QIDQ669971

Jian-Fa Qian, Li-Na Zhang

Publication date: 15 March 2019

Published in: Quantum Information Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11128-019-2197-6

zbMATH Keywords

cyclic codeMDS codeentanglement-assisted quantum code

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Other types of codes (94B60) Cyclic codes (94B15) Quantum coherence, entanglement, quantum correlations (81P40) Quantum coding (general) (81P70)

Related Items (34)

Four classes of new entanglement-assisted quantum optimal codes ⋮ MDS codes with euclidean and Hermitian hulls of flexible dimensions and their applications to EAQECCs ⋮ Entanglement-assisted quantum codes from cyclic codes and negacyclic codes ⋮ Entanglement-assisted quantum MDS codes from cyclic codes ⋮ New entanglement-assisted quantum constacyclic codes ⋮ Two families of entanglement-assisted quantum MDS codes from constacyclic codes ⋮ Steane enlargement of entanglement-assisted quantum error-correcting codes ⋮ \(l\)-LCP of codes and their applications to EAQEC codes ⋮ Some construction of entanglement-assisted quantum MDS codes ⋮ New entanglement-assisted quantum MDS codes with larger minimum distance ⋮ Some new entanglement-assisted quantum error-correcting MDS codes from generalized Reed-Solomon codes ⋮ New entanglement-assisted quantum MDS codes with length \(n = \frac{q^2+1}{5}\) ⋮ New classes of entanglement-assisted quantum MDS codes ⋮ New MDS EAQECCs from constacyclic codes over finite non-chain rings ⋮ New EAQMDS codes constructed from negacyclic codes ⋮ Three classes of new EAQEC MDS codes ⋮ Two families of entanglement-assisted quantum codes constructed from cyclic codes ⋮ A class of Hermitian dual-containing constacyclic codes and related quantum codes ⋮ Several new families of MDS EAQECCs with much larger dimensions and related application to EACQCs ⋮ Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2 ⋮ Cyclic codes and some new entanglement-assisted quantum MDS codes ⋮ Two families of entanglement-assisted quantum MDS codes from cyclic codes ⋮ Some new entanglement-assisted quantum error-correcting MDS codes with length \(\frac{q^2+1}{13} \) ⋮ New entanglement-assisted quantum MDS codes ⋮ Entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes ⋮ New entanglement-assisted quantum MDS codes derived from generalized Reed-Solomon codes ⋮ Hermitian hulls of constacyclic codes and a new family of entanglement-assisted quantum MDS codes ⋮ On the constructions of entanglement-assisted quantum MDS codes ⋮ Two classes of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes ⋮ Some new families of entanglement-assisted quantum MDS codes derived from negacyclic codes ⋮ Maximal entanglement EAQECCs from cyclic and constacyclic codes over \(\mathbb{F}_q+v_1\mathbb{F}_q+\cdots +v_{s-1}\mathbb{F}_q\) ⋮ Application of GRS codes to some entanglement-assisted quantum MDS codes ⋮ Entanglement-assisted quantum error correction codes with length \(n=q^2+1\) ⋮ Hermitian hulls of constacyclic codes and their applications to quantum codes

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