MDS codes with Galois hulls of arbitrary dimensions and the related entanglement-assisted quantum error correction
M Cao - IEEE Transactions on Information Theory, 2021 - ieeexplore.ieee.org
Let be a prime power and be an integer with. The-Galois hull of classical linear codes is a
generalization of the Euclidean hull and Hermitian hull. We provide a necessary and …
generalization of the Euclidean hull and Hermitian hull. We provide a necessary and …
On the hull-variation problem of equivalent linear codes
H Chen - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
The intersection () of a linear code and its Euclidean dual (Hermitian dual) is called the
Euclidean (Hermitian) hull of this code. It is natural to consider the hull-variation problem …
Euclidean (Hermitian) hull of this code. It is natural to consider the hull-variation problem …
New MDS entanglement-assisted quantum codes from MDS Hermitian self-orthogonal codes
H Chen - Designs, Codes and Cryptography, 2023 - Springer
Abstract The intersection C∩ C⊥ H of a linear code C⊂ F q 2 n and its Hermitian dual C⊥
H is called the Hermitian hull of this code. A linear code C⊂ F q 2 n satisfying C⊂ C⊥ H is …
H is called the Hermitian hull of this code. A linear code C⊂ F q 2 n satisfying C⊂ C⊥ H is …
Constructing quantum error-correcting codes that require a variable amount of entanglement
In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the
sender and the receiver have access to noiseless pre-shared entanglement. With this …
sender and the receiver have access to noiseless pre-shared entanglement. With this …
A new family of EAQMDS codes constructed from constacyclic codes
In this paper, a family of new entanglement-assisted quantum error-correcting codes
(EAQECCs) is constructed from constacyclic codes with length n= q 2+ 1 a by giving a new …
(EAQECCs) is constructed from constacyclic codes with length n= q 2+ 1 a by giving a new …
On linear codes with one-dimensional Euclidean hull and their applications to EAQECCs
L Sok - IEEE Transactions on Information Theory, 2022 - ieeexplore.ieee.org
The Euclidean hull of a linear code is the intersection of with its Euclidean dual. The hull with
low dimensions gets much interest due to its crucial role in determining the complexity of …
low dimensions gets much interest due to its crucial role in determining the complexity of …
Relative hulls and quantum codes
SE Anderson, E Camps-Moreno… - IEEE Transactions …, 2024 - ieeexplore.ieee.org
Given two-ary codes and, the relative hull of with respect to is the intersection. We prove that
when, the relative hull dimension can be repeatedly reduced by one, down to a certain …
when, the relative hull dimension can be repeatedly reduced by one, down to a certain …
How much entanglement does a quantum code need?
In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the
sender and the receiver have access to pre-shared entanglement. Such codes promise …
sender and the receiver have access to pre-shared entanglement. Such codes promise …
Entanglement-assisted quantum communication beating the quantum Singleton bound
M Grassl - Physical Review A, 2021 - APS
Brun, Devetak, and Hsieh [Science 314, 436 (2006) 10.1126/science. 1131563]
demonstrated that preshared entanglement between the sender and receiver enables …
demonstrated that preshared entanglement between the sender and receiver enables …
Cyclic codes and some new entanglement-assisted quantum MDS codes
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in
protecting quantum information from decoherence and quantum noise. In this work, we …
protecting quantum information from decoherence and quantum noise. In this work, we …