A Generalized Covering Algorithm for Chained Codes

The covering radius is a fundamental property of linear codes that characterizes the trade-off between storage and access in linear data-query protocols. The generalized covering radius was recently defined by Elimelech and Schwartz for applications in joint-recovery of linear data-queries. In this...

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Bibliographic Details
Main Authors Langton, Ben, Raviv, Netanel
Format Journal Article
LanguageEnglish
Published 08.05.2023
Subjects
Computer Science - Information Theory
Mathematics - Information Theory
Online AccessGet full text
DOI10.48550/arxiv.2305.05157

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Summary:The covering radius is a fundamental property of linear codes that characterizes the trade-off between storage and access in linear data-query protocols. The generalized covering radius was recently defined by Elimelech and Schwartz for applications in joint-recovery of linear data-queries. In this work we extend a known bound on the ordinary covering radius to the generalized one for all codes satisfying the chain condition -- a known condition which is satisfied by most known families of codes. Given a generator matrix of a special form, we also provide an algorithm which finds codewords which cover the input vectors within the distance specified by the bound. For the case of Reed-Muller codes we provide efficient construction of such generator matrices, therefore providing a faster alternative to a previous generalized covering algorithm for Reed-Muller codes.
DOI:10.48550/arxiv.2305.05157