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Quantum Information Processing

Some constructions of quantum MDS codes and EAQMDS codes from GRS codes

  • 01-07-2024
Published in:
Authors
Fuyin Tian
Lanqiang Li
Tingting Wu
Xiaojing Chen
Published in
Quantum Information Processing | Issue 7/2024

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Abstract

The article delves into the construction of quantum MDS codes and EAQMDS codes from Generalized Reed-Solomon (GRS) codes, a pivotal advancement in quantum error correction. It begins with an introduction to the necessity of quantum error-correcting codes in preserving quantum information integrity. The paper then explores the evolution of quantum codes, from Shor's initial work to the CSS construction and nonbinary quantum codes. The focus shifts to the quantum singleton bound and the construction of QMDS codes, with a particular emphasis on GRS codes. The article also introduces entanglement-assisted quantum error-correcting codes (EAQECCs) and EAQMDS codes, detailing how these can be constructed using GRS codes with varying parameters. Through several theorems and lemmas, the authors present new constructions of QMDS codes and EAQMDS codes, demonstrating the flexibility and power of GRS codes in enhancing quantum communication and computing. The paper concludes by summarizing the significance of these constructions and their potential impact on the field of quantum information science.
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previous article Quantum and LCD codes from skew constacyclic codes over a general class of non-chain rings
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Title
Some constructions of quantum MDS codes and EAQMDS codes from GRS codes
Authors
Fuyin Tian
Lanqiang Li
Tingting Wu
Xiaojing Chen
Publication date
01-07-2024
Publisher
Springer US
Published in
Quantum Information Processing / Issue 7/2024
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-024-04487-7
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