Application of Constacyclic Codes to Quantum MDS Codes
From MaRDI portal
Publication:2978750
DOI10.1109/TIT.2015.2388576zbMath1359.81088arXiv1403.2499OpenAlexW2078893330MaRDI QIDQ2978750
San Ling, Bocong Chen, Guang-Hui Zhang
Publication date: 28 April 2017
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1403.2499
Related Items (only showing first 100 items - show all)
Some new quantum MDS codes derived from generalized Reed-Solomon codes ⋮ The maximum designed distances of dual-containing non-primitive BCH codes ⋮ Hulls of constacyclic codes over finite non-chain rings and their applications in quantum codes construction ⋮ Some new quantum codes from constacyclic codes ⋮ New quantum codes from the images of cyclic codes ⋮ Quantum and LCD codes from skew constacyclic codes over a finite non-chain ring ⋮ Hermitian 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 codes ⋮ Optimal quinary negacyclic codes with minimum distance four ⋮ A class of Hermitian dual-containing constacyclic codes and related quantum codes ⋮ Duality of constacyclic codes of prime power length over the finite non-commutative chain ring \(\frac{ \mathbb{F}_{p^m} [ u , \theta }{ \langle u^2 \rangle} \)] ⋮ Construction of some new quantum MDS codes ⋮ Some constructions of quantum MDS codes ⋮ On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes ⋮ New entanglement-assisted quantum codes from \(k\)-Galois dual codes ⋮ On the minimum distance of negacyclic codes with two zeros ⋮ Quantum BCH codes with maximum designed distance ⋮ \(\mathbb{F}_q\)-linear skew cyclic codes over \(\mathbb{F}_{q^2}\) and their applications of quantum codes construction ⋮ On MDS linear complementary dual codes and entanglement-assisted quantum codes ⋮ New \(q\)-ary quantum MDS codes with distances bigger than \(\frac{q}{2}\) ⋮ \(u\)-constacyclic codes over \(\mathbb F_p+u\mathbb F_p\) and their applications of constructing new non-binary quantum codes ⋮ On \(\sigma \)-self-orthogonal constacyclic codes over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) ⋮ Two new classes of quantum MDS codes ⋮ Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance ⋮ MDS and near-MDS codes via twisted Reed-Solomon codes ⋮ Constacyclic codes over finite commutative semi-simple rings ⋮ On the construction of quantum constacyclic codes ⋮ Some quantum MDS codes with large minimum distance from generalized Reed-Solomon codes ⋮ A class of negacyclic BCH codes and its application to quantum codes ⋮ Quantum MDS codes with relatively large minimum distance from Hermitian self-orthogonal codes ⋮ Construction of new quantum codes derived from constacyclic codes over \(\mathbb{F}_{q^2}+u\mathbb{F}_{q^2}+\cdots +u^{r-1}\mathbb{F}_{q^2}\) ⋮ A class of constacyclic BCH codes ⋮ Improved constructions for quantum maximum distance separable codes ⋮ A class of constacyclic BCH codes and new quantum codes ⋮ On the distance of stabilizer quantum codes from \(J\)-affine variety codes ⋮ A different construction for some classes of quantum MDS codes ⋮ The Hermitian dual-containing LCD BCH codes and related quantum codes ⋮ New quantum codes from two linear codes ⋮ Nonbinary quantum codes from constacyclic codes over polynomial residue rings ⋮ New EAQEC codes from cyclic codes over \(\mathbb{F}_q + u\mathbb{F}_q\) ⋮ Entanglement-assisted quantum codes from cyclic codes and negacyclic codes ⋮ Quantum codes from codes over the ring \(\mathbb{F}_q + \alpha\mathbb{F}_q\) ⋮ New quantum MDS codes over finite fields ⋮ New EAQEC codes constructed from Galois LCD codes ⋮ New entanglement-assisted quantum constacyclic codes ⋮ A class of constacyclic codes are generalized Reed-Solomon codes ⋮ Quantum MDS codes with new length and large minimum distance ⋮ Quantum MDS and synchronizable codes from cyclic codes of length \(5p^s\) over \(\mathbb{F}_{p^m}\) ⋮ Two families of entanglement-assisted quantum MDS codes from constacyclic codes ⋮ Two classes of quantum codes from almost MDS codes ⋮ New quantum MDS codes with large minimum distance and short length from generalized Reed-Solomon codes ⋮ \((x^n - (a+bw), \xi, \eta)\)-skew constacyclic codes over \(\mathbb{F}_q + w\mathbb{F}_q\) and their applications in quantum codes ⋮ Construction of quantum MDS codes from generalized Reed–Solomon codes ⋮ Some construction of entanglement-assisted quantum MDS codes ⋮ The images of constacyclic codes and new quantum codes ⋮ Quantum bicyclic hyperbolic codes ⋮ New quantum codes from constacyclic and additive constacyclic codes ⋮ Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length \(3p^s\) ⋮ New MDS entanglement-assisted quantum codes from MDS Hermitian self-orthogonal codes ⋮ Two new classes of Hermitian self-orthogonal non-GRS MDS codes and their applications ⋮ Three classes of optimal Hermitian dual-containing codes and quantum codes ⋮ New quantum codes from constacyclic codes over a non-chain ring ⋮ Three classes of new EAQEC MDS codes ⋮ Quantum codes from Hermitian dual-containing constacyclic codes over \(\mathbb{F}_{q^2} + v\mathbb{F}_{q^2}\) ⋮ EAQEC codes from two distinct constacyclic codes ⋮ Entanglement-assisted quantum MDS codes constructed from negacyclic codes ⋮ A family of Hermitian dual-containing constacyclic codes and related quantum codes ⋮ On new quantum codes from matrix product codes ⋮ Improved constructions for nonbinary quantum BCH codes ⋮ Construction of new quantum MDS codes derived from constacyclic codes ⋮ MDS constacyclic codes of prime power lengths over finite fields and construction of quantum MDS codes ⋮ Construction of quantum negacyclic BCH codes ⋮ Quantum codes from a class of constacyclic codes over finite commutative rings ⋮ Some families of optimal quantum codes derived from constacyclic codes ⋮ New quantum codes from Hermitian dual-containing codes ⋮ New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes ⋮ New entanglement-assisted MDS quantum codes from constacyclic codes ⋮ On the construction of quantum MDS codes ⋮ Application of Hermitian self-orthogonal GRS codes to some quantum MDS codes ⋮ Quantum codes from repeated-root cyclic and negacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m} \) ⋮ Two families of entanglement-assisted quantum MDS codes from cyclic codes ⋮ Some new entanglement-assisted quantum error-correcting MDS codes with length \(\frac{q^2+1}{13} \) ⋮ Application of constacyclic codes over the semi local ring \(F_{p^m} + vF_{p^m}\) ⋮ Entanglement-assisted quantum MDS codes from negacyclic codes ⋮ New quantum codes from dual-containing cyclic codes over finite rings ⋮ Three new classes of optimal frequency-hopping sequence sets ⋮ Constacyclic 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 codes ⋮ New quantum MDS code from constacyclic codes ⋮ Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes ⋮ Quantum MDS codes from BCH constacyclic codes ⋮ Quantum MDS codes with large minimum distance ⋮ Quantum codes obtained from constacyclic codes ⋮ Some families of asymmetric quantum MDS codes constructed from constacyclic codes ⋮ Two families of BCH codes and new quantum codes ⋮ An application of constacyclic codes to entanglement-assisted quantum MDS codes ⋮ Quantum cyclic codes over \( \mathbb{Z}_m \) ⋮ The dual-containing primitive BCH codes with the maximum designed distance and their applications to quantum codes ⋮ New constructions of entanglement-assisted quantum MDS codes from negacyclic codes ⋮ Some new quantum MDS codes from generalized Reed-Solomon codes ⋮ A family of constacyclic codes over a class of non-chain rings \({\mathcal{A}}_{q,r}\) and new quantum codes ⋮ Three new classes of entanglement-assisted quantum MDS codes from cyclic codes
This page was built for publication: Application of Constacyclic Codes to Quantum MDS Codes