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
Published inProceedings / IEEE International Symposium on Information Theory pp. 844 - 849
Main Authors Langton, Ben, Raviv, Netanel
Format Conference Proceeding
LanguageEnglish
Published IEEE 25.06.2023
Subjects
Covering codes
Generators
Linear codes
Protocols
Reed-Muller codes
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ISSN2157-8117
DOI10.1109/ISIT54713.2023.10206543

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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 vector(s) 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.
ISSN:2157-8117
DOI:10.1109/ISIT54713.2023.10206543