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

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

Designs, Codes and Cryptography Pub Date : 2024-05-02 DOI:10.1007/s10623-024-01403-z

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

引用次数: 0

Abstract

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

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。

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

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.