具有大可用性的局部可恢复代码的构造

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

Designs, Codes and Cryptography Pub Date : 2025-04-05 DOI:10.1007/s10623-025-01624-w

Giacomo Micheli, Vincenzo Pallozzi Lavorante, Abhi Shukul, Noah Smith

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引用次数: 0

摘要

设p是质数，m是正整数，\(q=p^m\)。对于任意满足\(p\not \mid r(r+1)\)的固定局部性r，我们构造了无限的局部性可恢复码族，节点的可用性下界为\(q/r!+O(\sqrt{q})\)，局部性集的个数等于\(q^2/(r+1)!+O(q^{3/2})\)。

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Constructions of locally recoverable codes with large availability

Let p be a prime number, m be a positive integer, and \(q=p^m\). For any fixed locality r such that \(p\not \mid r(r+1)\), we construct infinite families of locally recoverable codes with availabilty of nodes lower bounded by \(q/r!+O(\sqrt{q})\) and number of locality sets equal to \(q^2/(r+1)!+O(q^{3/2})\).

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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.