On construction of quantum codes with dual-containing quasi-cyclic codes View Full Text


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Article Info

DATE

2022-07-26

AUTHORS

Chaofeng Guan, Ruihu Li, Liangdong Lu, Yang Liu, Hao Song

ABSTRACT

One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the construction of quantum codes over small fields. Firstly, some sufficient conditions for these 2-generator quasi-cyclic codes to be dual-containing concerning Hermitian inner product are determined. Then, we utilize these Hermitian dual-containing quasi-cyclic codes to produce quantum codes via the famous Hermitian construction. Moreover, we present a lower bound on the minimum distance of these quasi-cyclic codes, which is helpful to construct quantum codes with larger lengths and dimensions. As the computational results, many new quantum codes that exceed the quantum Gilbert-Varshamov bound are constructed over Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_q$$\end{document}, where q is 2, 3, 4, 5. In particular, 16 binary quantum codes raise the lower bound on the minimum distance in Grassl’s table (Grassl in bounds on the minimum distance of linear codes and quantum codes. http://www.codetables.de). In nonbinary cases, many quantum codes are new or have better parameters than those in the literature. More... »

PAGES

263

References to SciGraph publications

  • 2013-02-23. The structure of quaternary quantum caps in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2022-06-15. New Binary Quantum Codes Constructed from Quasi-Cyclic Codes in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 2019-11-26. Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 2020-07-30. Constructions of quasi-twisted quantum codes in QUANTUM INFORMATION PROCESSING
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    http://scigraph.springernature.com/pub.10.1007/s11128-022-03621-7

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    http://dx.doi.org/10.1007/s11128-022-03621-7

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