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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-21 DOI:10.1007/s10623-024-01421-x

Masaaki Harada

引用次数: 0

Abstract

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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构建四元赫尔墨斯自偶码的方法及其在量子码中的应用

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.