A construction of optimal quasi-cyclic locally recoverable codes using constituent codes

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI:10.1007/s10623-024-01532-5

Gustavo Terra Bastos, Angelynn Álvarez, Zachary Flores, Adriana Salerno

引用次数: 0

Abstract

A locally recoverable code of locality r over $\mathbb {F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most r other coordinates of that codeword. Locally recoverable codes are efficient at restoring corrupted messages and data which make them highly applicable to distributed storage systems. Quasi-cyclic codes of length $n=m\ell $ and index $\ell $ are linear codes that are invariant under cyclic shifts by $\ell $ places. In this paper, we decompose quasi-cyclic locally recoverable codes into a sum of constituent codes where each constituent code is a linear code over a field extension of $\mathbb {F}_q$. Using these constituent codes with set parameters, we propose conditions which ensure the existence of almost optimal and optimal quasi-cyclic locally recoverable codes with increased dimension and code length.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

求助全文

约1分钟内获得全文去求助

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.

期刊最新文献

The support designs of several families of lifted linear codes Low-weight codewords in cyclic codes A class of permutations on $${\mathbb {Z}}_{p}$$ with differential uniformity at most 3 A construction of optimal quasi-cyclic locally recoverable codes using constituent codes On automorphism groups of binary cyclic codes