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J. Hefei Univ. Tech. (Nat. Sci.)

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

Competent Authorities: Ministry of Education of the People's Republic of China

Sponsor by: Hefei University of Technology

ISSN 1000-1646, CN 34-1001/N

Structure of quantum repeated-root cyclic codes of length $ 4p^{s} $

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构造长度为 $ 4p^{s} $ 的量子重根循环码

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Oct.2023, Vol.46 No.10: 1430-1434

DOI: 10.3969/j.issn.1003-5060.2023.10.020

Authors

WANG Yuting, LIU Li

(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: In this paper, the repeated-root cyclic codes of length $ 4p^{s} $ over $ F_{p^{m}} $ which contain their dual codes are studied. Based on algebraic structure of the repeated-root cyclic codes, a necessary and sufficient condition for the repeated-root cyclic codes of length $ 4p^{s} $ over $ F_{p^{m}} $ which contain their dual codes is given, and their minimum distance is determined. Based on Steane's enlargement construction, several kinds of non-binary quantum codes with better parameters are constructed.

Keywords: quantum codes; dual codes; Hamming distance; cyclic codes; Steane's enlargement construction

作者信息

汪余婷，刘丽

（合肥工业大学数学学院，安徽合肥230601）

摘要和关键词

摘要: 文章研究 $ F_{p^{m}} $ 上码长是 $ 4p^{s} $ 重根循环码的对偶包含性;基于重根循环码的代数结构,给出 $ F_{p^{m}} $ 上码长是 $ 4p^{s} $ 重根循环码是对偶包含码的充要条件,并确定了它们的最小距离;基于 Steane 扩展构造,构造了几类参数较好的非二元量子码。

关键词: 量子码；对偶码；汉明距离；循环码；Steane扩展构造

Funding

国家自然科学基金资助项目（11871187）

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