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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Some New Quantum BCH Codes over Finite Fields.

Lijuan Xing1, Zhuo Li1

  • 1The State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China .

Entropy (Basel, Switzerland)
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces new quantum error correcting codes (QECCs) using Bose-Chaudhuri-Hocquenghem (BCH) codes. These novel quantum BCH codes offer improved parameters and broader applicability across finite fields.

Keywords:
BCH codescyclotomic cosetsdual codesquantum stabilizer codes

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Area of Science:

  • Quantum Information Science
  • Coding Theory
  • Quantum Computing

Background:

  • Quantum error correcting codes (QECCs) are crucial for mitigating quantum information decoherence.
  • Classical error correcting codes have been foundational in constructing quantum stabilizer codes.

Purpose of the Study:

  • To construct novel nonbinary quantum BCH codes using classical BCH codes over finite fields.
  • To explore the utility of cyclotomic cosets in the study and construction of quantum BCH codes.
  • To develop new families of quantum codes via established construction methods.

Main Methods:

  • Utilizing classical Bose-Chaudhuri-Hocquenghem (BCH) codes that contain their dual codes.
  • Employing cyclotomic cosets to identify suitable classical BCH codes.
  • Applying Steane's enlargement and Hermitian constructions for quantum code families.
  • Analyzing defining sets for consecutive integers to optimize code properties.

Main Results:

  • Successfully constructed nonbinary quantum BCH codes with specific parameter sets.
  • Demonstrated that cyclotomic cosets are effective tools for analyzing quantum BCH codes.
  • Achieved new quantum BCH codes with superior parameters and minimum distance bounds compared to existing literature.
  • Developed quantum codes constructible over any finite field, expanding their scope.

Conclusions:

  • Cyclotomic cosets provide a powerful framework for studying and constructing quantum BCH codes.
  • The newly developed quantum BCH codes exhibit enhanced performance and flexibility.
  • This research significantly advances the field of quantum error correction by providing more robust and versatile codes.