Computing sharp recovery structures for locally recoverable codes

Marquez-Corbella Irene; Martinez-Moro Edgar; Munuera Carlos

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Computing sharp recovery structures for locally recoverable codes

机译：计算临时可恢复代码的急剧恢复结构

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摘要

A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery structure as concise as possible for an arbitrary linear code C and a recovery method that realizes it. This algorithm also provides the locality and the dual distance of C. Complexity issues are studied as well. Several examples are included.

机译：局部可恢复的代码是错误校正代码，使得可以从其他坐标的小子集中恢复码字的单个坐标中的任何擦除。在本文中，我们开发一种算法，该算法将恢复结构计算为任意线性码C和实现它的恢复方法的简洁。该算法还提供了C的局部性和双距离。也研究了复杂性问题。包括几个例子。

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来源
《Designs, Codes and Crytography》 |2020年第8期|1687-1698|共12页
作者
Marquez-Corbella Irene; Martinez-Moro Edgar; Munuera Carlos;
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作者单位

Univ La Laguna Dept Math Stat & O Res Tenerife 38200 Spain;

Univ Valladolid Inst Math Campus Miguel Delibes Valladolid 47011 Castilla Spain;

Univ Valladolid Dept Appl Math Avda Salamanca SN Valladolid 47014 Castilla Spain;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Error-correcting code; Locally recoverable code; Sharp recovery structures;

机译：纠错代码;本地可恢复的代码;急剧恢复结构;

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专利

1. A Tight Rate Bound and Matching Construction for Locally Recoverable Codes With Sequential Recovery From Any Number of Multiple Erasures [J] . IEEE Transactions on Information Theory . 2020,第2期

机译：具有任意多次多重删除顺序恢复能力的本地可恢复代码的紧速率约束和匹配构造
2. Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes [J] . Lopez Hiram H., Matthews Gretchen L., Soprunov Ivan Designs, Codes and Crytography . 2020,第8期

机译：单体 - 笛卡尔码及其双重，应用于LCD代码，量子代码和本地可收回的代码
3. RS-like locally recoverable codes with intersecting recovering sets [J] . Rajput Charul, Bhaintwal Maheshanand Finite fields and their applications . 2020,第Deca期

机译：与交叉恢复集的RS样本地可恢复的代码
4. A tight rate bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures [C] . S. B. Balaji, Ganesh R. Kini, P. Vijay Kumar IEEE International Symposium on Information Theory . 2017

机译：严格的速率范围和本地可恢复代码的匹配结构，可从任意多次擦除中顺序恢复
5. Locally Recoverable Codes From Algebraic Curves [D] . Ballentine, Sean. 2018

机译：来自代数曲线的本地可恢复的代码
6. Multi-Shot Sensitivity-Encoded Diffusion Data Recovery Using Structured Low-Rank Matrix Completion (MUSSELS) [O] . Merry Mani, Mathews Jacob, Douglas Kelley, -1

机译：使用结构化低秩矩阵补全（MUSSELS）进行多发敏感度编码的扩散数据恢复
7. Computing sharp recovery structures for locally recoverable codes [O] . Irene Márquez-Corbella, Edgar Martínez-Moro, Carlos Munuera 2020

机译：计算临时可恢复代码的急剧恢复结构
8. Generalized Method for One-Way Coupling of CTH and Lagrangian Finite Element Codes with Complex Structures using the Interdisciplinary Computing Environment. [R] . Clarke, J. A., Namburu, R. R. 2004

机译：利用跨学科计算环境进行复杂结构CTH与拉格朗日有限元单向耦合的广义方法。

Computing sharp recovery structures for locally recoverable codes

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