The Subfield Metric and its Application to Quantum Error Correction

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2023-11-02 DOI:10.1142/s021949882550063x

Markus Grassl, Anna-Lena Horlemann, Violetta Weger

引用次数: 0

Abstract

We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.

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子域度量及其在量子纠错中的应用

在有限扩展域上引入了一种新的权值和相应的度量，用于非对称误差校正。权重区分了基场和基场之外的元素，这是由非对称量子代码驱动的。我们建立了该权重和度量的理论框架，包括上界和下界，随机码的渐近行为，并证明了一个达到单态上界的最优码族的存在性。

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

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.