New quantum codes derived from images of cyclic codes View Full Text


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Article Info

DATE

2022-07-26

AUTHORS

Shixin Zhu, Hongzhe Guo, Xiaoshan Kai, Zhonghua Sun

ABSTRACT

Let q be a prime power and m≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m \ge 2$$\end{document} be a positive integer. Based on classical cyclic codes, we construct new quantum codes by using images of cyclic codes. Three classes of quantum codes are derived from the Fq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{q^2}$$\end{document} images of cyclic codes over Fq2m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{q^{2m}}$$\end{document}. Compared with the known ones, these new quantum codes have larger minimum distance or higher code rate. More... »

PAGES

254

References to SciGraph publications

  • 2020-03-16. Entanglement-assisted quantum codes from cyclic codes and negacyclic codes in QUANTUM INFORMATION PROCESSING
  • 2011-08-03. Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes in QUANTUM INFORMATION PROCESSING
  • 2020-06-11. The images of constacyclic codes and new quantum codes in QUANTUM INFORMATION PROCESSING
  • 2019-02-09. Two new families of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes in QUANTUM INFORMATION PROCESSING
  • 2019-03-22. New quantum constacyclic codes in QUANTUM INFORMATION PROCESSING
  • 2021-03-13. Four classes of new entanglement-assisted quantum optimal codes in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2020-06-10. New entanglement-assisted quantum MDS codes with length n=q2+15 in QUANTUM INFORMATION PROCESSING
  • 2020-05-22. On Steane-enlargement of quantum codes from Cartesian product point sets in QUANTUM INFORMATION PROCESSING
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    http://scigraph.springernature.com/pub.10.1007/s11128-022-03603-9

    DOI

    http://dx.doi.org/10.1007/s11128-022-03603-9

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