来自单项式-笛卡尔码及其子域-子码的最优 $$(r,\delta )$$ -LRCs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-02 DOI:10.1007/s10623-024-01403-z

C. Galindo, F. Hernando, H. Martín-Cruz

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引用次数: 0

摘要

我们研究的单项式笛卡尔码（MCCs）可被视为（(r,\delta )\）-本地可恢复码（LRCs）。这些编码对它们的最小距离有一个自然的约束，我们确定了那些在这个距离上产生$(r,\delta )$-最优LRC的编码，它们实际上是$(r,\delta )$-最优的。MCC的一个大的子族允许在较小的支持域上具有与某些最优MCC相同的参数的子域子码。这一事实允许我们确定无限多组新的（(r,\delta )）最优 LRC 及其参数。

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$Optimal $$(r,\delta )$$ -LRCs from monomial-Cartesian codes and their subfield-subcodes$

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Optimal $$(r,\delta )$$ -LRCs from monomial-Cartesian codes and their subfield-subcodes

We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,\delta )$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,\delta )$-optimal LRCs for that distance, which are in fact $(r,\delta )$-optimal. A large subfamily of MCCs admits subfield-subcodes with the same parameters of certain optimal MCCs but over smaller supporting fields. This fact allows us to determine infinitely many sets of new $(r,\delta )$-optimal LRCs and their parameters.

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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.