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Quantum Information Processing

Galois self-orthogonal and Galois LCD one-generator -monomial codes

  • 01-11-2025
Published in:
Authors
Oussama Kabbouch
Lhousain Mouatadid
Mustapha Najmeddine
Nuh Aydin
Published in
Quantum Information Processing | Issue 11/2025

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Abstract

This article delves into the construction and analysis of Galois self-orthogonal and linear complementary dual (LCD) one-generator monomial codes, which are crucial for quantum error correction. The study explores the use of skew polynomial rings and their properties to derive these codes, providing necessary and sufficient conditions for Galois self-orthogonality and the LCD property. The article also presents computational results, including new quantum error-correcting codes and entanglement-assisted quantum error-correcting codes, derived from these monomial codes. Additionally, it discusses the application of the CSS construction method to generate these codes, highlighting their potential in enhancing quantum communication and computation. The findings are supported by detailed mathematical derivations and practical examples, making it a comprehensive resource for professionals in the field.
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previous article An efficient and verifiable quantum secret sharing scheme based on a novel seven-qubit entangled state
next article Maximum and minimum relative entropies of imaginarity
Title
Galois self-orthogonal and Galois LCD one-generator -monomial codes
Authors
Oussama Kabbouch
Lhousain Mouatadid
Mustapha Najmeddine
Nuh Aydin
Publication date
01-11-2025
Publisher
Springer US
Published in
Quantum Information Processing / Issue 11/2025
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-025-04967-4
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