New entanglement-assisted quantum codes from \(k\)-Galois dual codes
From MaRDI portal
Publication:1633280
DOI10.1016/j.ffa.2018.09.001zbMath1404.94138OpenAlexW2891992737WikidataQ129211707 ScholiaQ129211707MaRDI QIDQ1633280
Peng Hu, Long Yu, Xiu-sheng Liu
Publication date: 19 December 2018
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.ffa.2018.09.001
Linear codes (general theory) (94B05) Combinatorial codes (94B25) Quantum coherence, entanglement, quantum correlations (81P40) Quantum coding (general) (81P70)
Related Items (38)
New constructions of entanglement-assisted quantum codes ⋮ Asymmetric entanglement-assisted quantum codes: bound and constructions ⋮ \(\mathbb{F}_q\)-linear skew cyclic codes over \(\mathbb{F}_{q^2}\) and their applications of quantum codes construction ⋮ On \(\sigma \)-self-orthogonal constacyclic codes over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) ⋮ New Galois hulls of generalized Reed-Solomon codes ⋮ New quantum codes from two linear codes ⋮ New EAQEC codes from cyclic codes over \(\mathbb{F}_q + u\mathbb{F}_q\) ⋮ Three new classes of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes ⋮ Entanglement-assisted quantum MDS codes from cyclic codes ⋮ Quantum MDS and synchronizable codes from cyclic codes of length \(5p^s\) over \(\mathbb{F}_{p^m}\) ⋮ New entanglement-assisted quantum MDS codes with larger minimum distance ⋮ New entanglement-assisted quantum MDS codes with length \(n = \frac{q^2+1}{5}\) ⋮ Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length \(3p^s\) ⋮ Constructions of symplectic LCD MDS codes from quasi-cyclic codes ⋮ New EAQMDS codes constructed from negacyclic codes ⋮ Three classes of new EAQEC MDS codes ⋮ Several new families of MDS EAQECCs with much larger dimensions and related application to EACQCs ⋮ Matrix-product codes related to constacyclic codes and their applications to EAQEC codes ⋮ An open problem of \(k\)-Galois hulls and its application ⋮ Cyclic codes and some new entanglement-assisted quantum MDS codes ⋮ Constructions of new entanglement-assisted quantum MDS and almost MDS codes ⋮ A new family of EAQMDS codes constructed from constacyclic codes ⋮ Quantum codes and entanglement-assisted quantum codes derived from one-generator quasi-twisted codes ⋮ New entanglement-assisted quantum MDS codes ⋮ Constructing MDS Galois self-dual constacyclic codes over finite fields ⋮ Galois hulls of linear codes over finite fields ⋮ Entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes ⋮ Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes ⋮ Self-reciprocal and self-conjugate-reciprocal irreducible factors of \(x^n - \lambda\) and their applications ⋮ Hermitian hulls of constacyclic codes and a new family of entanglement-assisted quantum MDS codes ⋮ Linear \(\ell\)-intersection pairs of MDS codes and their applications to AEAQECCs ⋮ On the constructions of entanglement-assisted quantum MDS codes ⋮ Galois self-dual extended duadic constacyclic codes ⋮ Quantum MDS and synchronizable codes from cyclic and negacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m}\) ⋮ QEC and EAQEC codes from cyclic codes over non-chain rings ⋮ Maximal entanglement-assisted quantum error correction codes from the skew group ring \(\mathbb{F}_4\rtimes_\varphi G\) by a heuristic search scheme ⋮ Construction of new entanglement-assisted quantum MDS codes via cyclic codes ⋮ Galois self-orthogonal constacyclic codes over finite fields
Cites Work
- Unnamed Item
- Entanglement-assisted quantum codes from arbitrary binary linear codes
- The combinatorics of LCD codes: linear programming bound and orthogonal matrices
- Galois LCD codes over finite fields
- Constructions of good entanglement-assisted quantum error correcting codes
- Constructions of optimal LCD codes over large finite fields
- Quantum codes from linear codes over finite chain rings
- Galois self-dual constacyclic codes
- Application of Constacyclic Codes to Quantum MDS Codes
- Duality in Entanglement-Assisted Quantum Error Correction
- New Quantum MDS Codes From Negacyclic Codes
- Correcting Quantum Errors with Entanglement
- A new upper bound on the minimal distance of self-dual codes
- On Quantum and Classical BCH Codes
- Nonbinary quantum stabilizer codes
- Quantum error correction via codes over GF(4)
- New Quantum MDS Codes
- Application of Classical Hermitian Self-Orthogonal MDS Codes to Quantum MDS Codes
- Trellis structure and higher weights of extremal self-dual codes
This page was built for publication: New entanglement-assisted quantum codes from \(k\)-Galois dual codes