Constructions of good entanglement-assisted quantum error correcting codes

K Guenda, S Jitman, TA Gulliver - Designs, Codes and Cryptography, 2018‏ - Springer
Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and
fundamental class of codes. They allow for the construction of quantum codes from classical …

[کتاب][B] Concise encyclopedia of coding theory

WC Huffman, JL Kim, P Solé - 2021‏ - api.taylorfrancis.com
Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

MDS codes with hulls of arbitrary dimensions and their quantum error correction

G Luo, X Cao, X Chen - IEEE Transactions on Information …, 2018‏ - ieeexplore.ieee.org
The hull of linear codes has promising utilization in coding theory and quantum coding
theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended …

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

C Galindo, F Hernando, R Matsumoto… - Quantum Information …, 2019‏ - Springer
We prove that the known formulae for computing the optimal number of maximally entangled
pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over …

Euclidean and Hermitian hulls of MDS codes and their applications to EAQECCs

W Fang, FW Fu, L Li, S Zhu - IEEE Transactions on Information …, 2019‏ - ieeexplore.ieee.org
In this paper, we construct several classes of maximum distance separable (MDS) codes via
generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can …

Entropic proofs of Singleton bounds for quantum error-correcting codes

M Grassl, F Huber, A Winter - IEEE Transactions on Information …, 2022‏ - ieeexplore.ieee.org
We show that a relatively simple reasoning using von Neumann entropy inequalities yields a
robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC) …

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 …

Entanglement-assisted quantum MDS codes constructed from negacyclic codes

J Chen, Y Huang, C Feng, R Chen - Quantum Information Processing, 2017‏ - Springer
Recently, entanglement-assisted quantum codes have been constructed from cyclic codes
by some scholars. However, how to determine the number of shared pairs required to …

Linear programming bounds for entanglement-assisted quantum error-correcting codes by split weight enumerators

CY Lai, A Ashikhmin - IEEE Transactions on Information Theory, 2017‏ - ieeexplore.ieee.org
Linear programming approaches have been applied to derive upper bounds on the size of
classical and quantum codes. In this paper, we derive similar results for general quantum …

A survey of quantum error correction

R Matsumoto, M Hagiwara - IEICE Transactions on Fundamentals …, 2021‏ - search.ieice.org
A Survey of Quantum Error Correction Page 1 1654 IEICE TRANS. FUNDAMENTALS, VOL.E104–A,
NO.12 DECEMBER 2021 INVITED SURVEY PAPER A Survey of Quantum Error Correction …