构建四元赫尔墨斯自偶码的方法及其在量子码中的应用

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-05-21 DOI:10.1007/s10623-024-01421-x

Masaaki Harada

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引用次数: 0

摘要

我们介绍了作为四环编码的一种修正的四重修正四（\mu \）-环编码。我们给出了四元修饰四（\mu \）-环形赫米特自偶码的基本性质。我们还构造了具有较大最小权值的四元改进四（\mu \）-环形赫米特自偶码。我们首次构造了两种四元赫米蒂自偶码 [56, 28, 16]。这些码改进了之前已知的所有四元（线性）[56, 28] 码中最大最小权重的下限。此外，这些编码还意味着量子[[56, 0, 16]]编码的存在。

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A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes

We introduce quaternary modified four \(\mu \)-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four \(\mu \)-circulant Hermitian self-dual codes. We also construct quaternary modified four \(\mu \)-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual [56, 28, 16] codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) [56, 28] codes. In addition, these codes imply the existence of a quantum [[56, 0, 16]] code.

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.