Easy repair via codes with simplex locality

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-02-03 DOI:10.1016/j.ffa.2026.102809

M. Kuijper , J. Lieb , D. Napp

引用次数: 0

Abstract

In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements, measured by the code's rate, minimum distance, locality, availability as well as field size, influence each other and can not all be maximized at the same time. We focus on the notion of easy repair, more specifically on the construction of codes that can repair correctable erasure patterns with minimal computational effort. In particular, we introduce the easy repair property and then present binary codes of different rates that possess this property. The presented codes are all in some way related to binary simplex codes and include block codes as well as unit-memory convolutional codes. We also formulate conditions under which the easy repairs can be performed in parallel, thus improving access speed of the distributed storage system.

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通过具有单一局部性的代码容易修复

在分布式存储系统的环境中，本地可修复代码变得非常重要。在本文中，我们的重点是码，允许多擦除模式解码与低计算量。不同的最优性需求，由代码的速率、最小距离、局域性、可用性以及字段大小来衡量，它们相互影响，并且不能同时全部最大化。我们专注于容易修复的概念，更具体地说，是构建可以用最小的计算量修复可纠正的擦除模式的代码。特别地，我们引入了易修复特性，然后给出了具有该特性的不同速率的二进制码。所提出的代码都在某种程度上与二进制单纯形码有关，包括块码和单位内存卷积码。我们还制定了易维修并行进行的条件，从而提高了分布式存储系统的访问速度。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.